domingo, 27 de novembro de 2016

Claudio Costa: PHILOSOPHICAL TEXTS - TEXTOS DE FILOSOFIA



THIS "BLOG" IS THOUGHT AS A WAY TO MAKE MY WORK IN PHILOSOPHY ACCESSIBLE TO A WIDE PUBLICUM. THERE ARE MORE THAN 100 TEXTS, MOST OF THEM IN DRAFT FORM. MANY ARE INTRODUCTORY TEXTS. THE TEXTS MARKED WITH ONE OR MORE # ARE THOSE THAT CAN BE OF SOME INTEREST FOR THE SPECIALISTS. I HOPE IT IS USEFUL.

ESSE "BLOG" FOI PENSADO COMO UMA MANEIRA DE TORNAR MEU TRABALHO EM FILOSOFIA ACESSÍVEL A UM PÚBLICO MAIS AMPLO. SÃO MAIS DE 100 TEXTOS, A MAIORIA EM FORMA DE DRAFT. AQUELES MARCADOS COM UM OU MAIS # SÃO OS QUE PODEM SER DE ALGUM INTERESSE PARA A PESQUISA. OS TRABALHOS MAIS ANTIGOS E INTRODUTÓRIOS ESTÃO EM PORTUGUÊS. ESPERO QUE SEJAM ÚTEIS.

  On my CV:
  After a study of medicine I made my M.S. in philosophy at the UFRJ (Rio de Janeiro) with prof. Raul Landin. My PhD I made at the University of Konstanz (Germany) with Gottfried Gabriel and Friedrich Kambartel. Afterwards there were very useful one year post-doctoral works in the Hochschule für Philosophie (with Friedo Ricken), at the University of Berkeley (with John Searle) at the University of Oxford (with Richard Swinburne), at the University of Konstanz (with Wolfgang Spohn) and now at the University of Göteborg (with Anna-Sofia Maurin) and in the Institut Jean Nicod (with François Recanati). 
  My main articles published in international journals were collected and better developed in the book Lines of Thought: Rethinking Philosophical Assumptions (Cambridge Scholars Publishing, 2014). I also developed a short theory on the nature of philosophy in the book The Philosophical Inquiry (UPA, 2002). Presently I am writting a book aiming to recuperate the credibility of the old orthodoxy in analytic philosophy of language. This book, to be called Philosophical Semantics, will be also published by CSP probably in 2017.

  Presently I am full professor of philosophy and (mainly) a CNPq researcher at the UFRN, in the Northeast of Brazil.

  Finally, probably I have some degree of autism. Although there is nothing to recommend of my defective intelect, autism forces me to work in the independence of the leading beliefs that must be shared by the community of ideas in order to make it cohesive.

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#TROPE THEORY AND THE UNBEARABLE LIGHTNESS OF BEING



Appendix to chapter 3

DRAFT FOR THE BOOK 'PHILOSOPHICAL SEMANTICS' (Cambridge Scholars Publishing, 2017)

Appendix ch. 3


Trope Theory and the Unbearable Lightness of Being OriginalEla provém da consideração de que na definição da existência do pensamento não entra em questão a mente singular que o tem, nem a pessoa na qual ele ocorre.



Any possible world and, of course, this one, is completely constituted by its tropes.
D. C. Williams

‘Could you show me some properties (qualities, characteristics…) of the things around us?’ Asked in this way, any normal person would surely point to a few nearby objects, naming their properties (qualities, characteristics…), e.g., the yellowness of this sofa, the hardness of that wall, this property of my shirt of being made of cotton… Many traditional philosophers, however, would say that these things cannot really be properties in the strict sense of the word. For in this strict sense, properties are abstract entities, universals accessible only to our intellect, not to our senses.
   This comparison suggests that the ontological starting place of traditional ontological realism is opposed to the ontological starting place of the common man, and indeed of our own common sense in general. Common sense begins by considering as prototypical examples of properties the spatio-temporal properties directly given to us in perceptual experience, only afterwards considering those properties that are in some way derived from perceptual experience. The contemporary ontology that in its pure form sustains this view is trope theory. Properties are for trope theorists spatio-temporally located entities called ‘concretized properties’, ‘particularized qualities’, ‘individual accidents’, ‘quality-bytes’, ‘abstract particulars’ or simply tropes. According to trope theory, universal properties should be consequences of the ontological building blocks that are the spatio-temporally singularized properties called tropes, and not the other way round.
   The importance of the theory of tropes resides in the fact that after the development of nominalism already in the Middle Ages, this may turn out to be the only really ground-breaking advance in ontology. Although the concept of the trope as a singularized property has existed at least since Aristotle, only in the 1950s did an Australian philosopher named D. C. Williams conceive the bold idea of assigning tropes metaphysical pride of place as the most fundamental ontological building-blocks.[1] His central aim was to use the notion of trope to solve (or dissolve) the traditional problem of universals and to explain the nature of concrete particulars. In fact, pure trope-theory is a one-category ontology. Because of this, my hunch is that the theory of tropes is so revolutionarily simple in its fundamentals that it could produce an upheaval in ontology similar to that caused by the introduction of new physicalist theories to solve the mind-body problem in the second half of the twentieth century.
   In what follows, instead of doing the hard work of discussing different versions of trope theory, I will take the easier and more direct route of outlining the view that from our methodologically modest common-sense perspective seems the most plausible.

1. Introducing Tropes
First, what are tropes? Tropes can be elucidated as being properties individually located in space and enduring in time, whereby properties must be understood simply as empirical designata of predicative expressions. The most fundamental tropes, from a genetic-epistemological perspective, are those that are accessed by direct perceptual experience, like qualities. Examples of quality-tropes are the yellowness of this sofa, the smell of a particular daisy at a certain time and the snorting of a particular rhino trying to attract a female. Other tropes would be the red color of the Golden Gate Bridge, its weight, hardness, form, height above sea level… Tropes can be psychological properties, like feelings of pain, sorrow, love and pleasure (Williams, 1953: 17). We can prove the reality of tropes by considering that they can be objects of selective perception: looking at the ocean, one can concentrate alternately on its color-tropes, the form-tropes of its waves or their sound-tropes. Tropes usually appear combined with other tropes, and some conglomerates of different kinds of tropes are highly complex and to some extent dispositional. This is the case of Socrates’ psychological character, of biological properties like that of a certain cat of being a mammal, of social properties like that of India being a democratic country; they are all in some way spatio-temporally located, even if dependent on concrete physical things.
   Tropes differ from what I prefer to call individuals: things that must be unique and are referred by nominal terms like a daisy, a rhino, the Golden Gate Bridge and Socrates. Most of them are material objects. But some compositions of tropes are individuals, though not material objects. This is the case of a rainbow someone has pointed to and Beethoven’s 5th Symphony, which each consist of only one class of tropes and is referred to using singular terms. Finally, there are derivative tropes like the fundamental physical forces, even if from a purely physical perspective we can speculate as to whether all other tropes aren’t to some extent grounded on them (see Campbell 1990, ch. 6).
   Like all particulars, tropes have identity conditions. I suggest an ontological condition (a) followed by a linguistic requirement (b):

Tropes are identified by their (a) spatiotemporal existence to the extent that they display continuity over time (are continuous) and are amenable to certain direct or (mostly) indirect experiential ways and conditions of accessing them and (b) by being linguistically accessible by means of the predicative expressions of singular statements.

So understood tropes contrast mainly with material objects referred to by means of nominative expressions, particularly proper names.
   The linguistic requirement (b) has a guiding function: as spatio-temporally located properties, tropes can be designated by means of predicative expressions. Regarding the ontological condition (a) there is more to say. Consider the following example: the pair of shoes that I am wearing is brown. The right shoe’s property of being brown can be seen as a trope, since it displays continuity and is located on my right shoe, and the left shoe’s property of being brown can be seen as another trope, since it displays continuity and is located on my left shoe. Because these shoes have different spatial locations, we can regard them as displaying two tropes of the color brown. And because the relatively homogeneous continuity of the color of the right shoe, this color can be said to be a trope – a (located) property. The smoothness of my left shoe is also a trope that has the same location, homogeneity and maybe even the same duration of its brown color. Does this mean that this brown and this smooth are the same trope? No, since they are different kinds of tropes perceptually accessed through different perceptual ways and conditions of access.
   To the further question of how much my left shoe’s trope of brown can be subdivided, one possible answer would be: into as many unities as we can distinguish. But since according to perceptual distance and acuity we can distinguish different amounts, this does not seem to be very elucidating (see Campbell 1990: 136-7). Because of this – and again drawing on common sense and ordinary language – it seems better to say that the unity of a trope – which we can rightly call a property – would be established by the natural limits of its spatio-temporal continuity as being the same, disregarding its possible divisions. Thus, for instance, the whiteness of a wall could be considered a myriad of tropes if any visible point of whiteness were considered a trope; but considering a trope of whiteness to be the whole of its continuity, we are not only being economical but also following ordinary language practices, for we would rather say that this wall ‘has the property of being white’ than that it has a myriad of punctiform properties of whiteness. The size and form of the wall, on the other hand, are spatiotemporally well delimited, deserving to be individuated as tropes, once they are called properties as a point of convention within our usual language-games regarding medium sized dry objects. A related question concerns the duration of tropes. How long will my left shoe’s brown trope last? A reasonable answer is: it will probably survive no longer than my left shoe. A trope lasts as long as it remains essentially the same, while maintaining its spatio-temporal continuity.
   I mention all these things because hasty considerations can easily give rise to attempts to discredit identity conditions for tropes, for example, by pushing precision beyond its contextually reasonable bounds. The vagueness of our identity conditions for tropes is as much a direct consequence of the way we experience the world as of the way the world is supposed to be under assumed practices, allowing the constitution of a conceptual system with the suitable amount of precision. Moreover, many tropes (e.g. social tropes) are highly dispersed in space and time.
   Since tropes are any spatio-temporally situated properties, they are also existent particulars. Because existence – as we will see later in this book – can be seen as the effective applicability of a predicative ascription rule to at least one thing, by asserting existence we assume a need to spatio-temporally locate the trope or the set of tropes. Moreover, tropes are said to have a proper existence, even if unavoidably related to other tropes. This is exemplified by the colors of the rainbow, the sound of the wind, the smell of a daisy, etc. They differ only from other individuals due to their uniqueness.
   Are spatial forms and duration in time tropes? Well, these things cannot be found without being associated with tropes, a shape with a color, a volume with a weight, a duration in time with the continuous existence of some tropes or bundle of tropes... Keith Campbell, disagreeing with D. C. Williams, did not consider forms as tropes because of their dependence upon other tropes (Campbell 1981)[2].
   However, if we wish to preserve our one-category ontology, tropes are better understood as any spatio-temporally existents designated by means of predi­cative expressions and not necessarily as independent, primitive or simple proprieties, because these things can vary with the language-game (as we saw, for Wittgenstein the simple and the primitive are relative to the language-game). If we hold that view, a better answer emerges, since we can see forms and durations as limitations in space and time respectively. They would rise from limitations imposed by standard quality-tropes. Hence, it seems that we could view forms and durations as at least dependent kinds of tropes – let us call them limiting tropes.
   Another question is whether relations are tropes. Since relations are spatio-temporally located, though often only in a rather vague way, and since relations are designated by means of polyadic predicative expressions (usually dyadic), it seems that relations are tropes, even if their existence is subsidiary to the existence of their relata. There are different kinds of relations with different strengths and I cannot develop this point here. The most interesting relation is probably the causal one. For instance: ‘The throwing of a stone broke the window’. As Campbell noted, a causal relation is to be seen as a relation between tropes (1990, ch. 5.15). The relational predicate ‘…causes…’ is not between the objects stone and window, but between the throwing (of a stone) and the breaking (of the window), which are events that can be designated by means of predicates (‘The stone was throw’, ‘The window was broken’), being therefore tropes according to our identity condition. Moreover, the causal relation is called an internal relation, which is defined as a relation that exists as a consequence of the existence of their relata, given adequate conditions. A clearer case of an internal relation is that of strict similarity between two tropes. For instance: ‘The blue of this ocean is like the blue of the sky above it’. Once these two blues are given, the similarity follows. It may not be easy to admit, but strict similarity is also not only predicatively designated but also spatio-temporally located: it is in-between and not out there. Therefore it should also be classified as a relational trope, even if subsidiary to its relata, grounded on them.
   One objection against the idea that relations are tropes is that if relations are tropes then the relational trope and its relata must be related by a new relational trope and so on ad infinitum (Maurin 1992: 134 f.).[3] I will argue against this idea first by appealing to a reductio based on the insight that the same problem comes up again in the case of one-place predications. In other words, if a refers to an individual and b refers to another individual, and there is a relation aRb so that this relation produces an infinite regression, then the same should be true of a one-place predication of the form Fa, like in the statement ‘The Earth is round.’ That is, we would need a relation R to relate the object referred to by the nominal term ‘the Earth’ and the trope of roundness designated by the predicate ‘…is round’, symbolizing it as FRa; and this relation R would naturally require two new relations ‘FR1RR2a’ to relate R to their relata, and so on ad infinitum. But this seems absurd! Moreover, these relations seem to be empty and meaningless. If instead of ‘The Earth is round’ we say ‘The Earth is related with its roundness’, we would not be making any sense; the same with ‘The Earth is related with the relation of its relation with its roundness’. Thus, it is better to see the link between subject and predicate as a ‘non-relational tie’ (Strawson 1959, part II, Searle 1969: 113) or like the link of a chain, to use Wittgenstein’s metaphor. They are not tropes but pseudo-additions in the true sense of the word. I conclude that we don’t need to postulate FRa in order to explain Fa.[4] And if this seems obviously true of the monadic links represented by singular predicative sentences, there is no reason not to extend this result to dyadic and polyadic relations said to produce a Bradleyan regress. In my view, relations must be seen as linked with their relata in the same way as non-relational properties are linked with their objects. To see this, consider the following example: (i) ‘Socrates is a friend of Plato’. Since friendship is a relation, a Bradleyan would be entitled to replace sentence (i) with (ii): ‘Socrates has a relation of friendship with Plato’, which still says the same thing by specifying that friendship is a relation. But the Bradleyan would then go ahead, deriving from (ii) the sentence (iii) ‘Socrates relates itself to its relation of friendship relative to Plato’, which is an instantiation of aR1RR2b. But we see that (iii) hardly makes any sense.

2. Tropes and Universals
The theory of tropes is important because it promises a parsimonious solution for at least two perennial ontological problems: the problem of universals and the problem of concrete particulars.
   I begin with the problem of universals. Linguistically stated this problem consists in the question of how we can apply the same general term to many different particulars; and ontologically stated it consists in the question of how it is possible that many different particulars can share the same property. Traditional realist philosophers suggested that the only possible solution to this problem is to postulate that a general term refers to a universal understood as an abstract entity (existing ante rem or even in rebus, according to the version) that can in some way be instantiated in many particulars. Thus, for the realist we say that this rose and that strawberry are red because they instantiate or exemplify the universal of redness (red-in-itself). This solution, which goes back to Plato, has never rescued itself from unsolvable difficulties. After all, universal properties must be non-empirical abstract objects accessible only to the intellect. With this, we are left with two worlds: our empirical world and a world with an infinite number of abstract entities whose intelligibility is questionable and for which we have no identity criteria. Moreover, the realist is left with insoluble problems of how to explain the relation between these abstract entities and the particulars that instantiate them or even with our cognitive minds. On the other hand, if you ask a layman where properties are, he would answer by pointing to the blue of the sky, the hardness of a table, the softness of jelly… and not to a Platonist mood. This contrast leads us to the suspicion that only intensive philosophical training – supposedly originated from the ideological pressure of some mystical belief in what a Nietzschean would call a ‘a world of beyond’ (or Überwelt), a true temptation for unworldly creatures like philosophers – could succeed in conditioning one’s mind to see properties in such an idealized way.
   To solve the problem of universals by appealing to tropes, we need to introduce the idea of similarity, or resemblance or likeness between tropes, which could conceivably be understood as a kind of relational trope. Philosophers like D. C. Williams (1953: 9) and Keith Campbell (1981: 477-488) saw universals as classes of precisely similar tropes. Thus, the universal ‘red’ refers to the class of all tropes of red, which are unified by the fact that these tropes all have the internal relation of being precisely similar one with the other. For Williams, when we say, ‘This rose is red’, we mean that this rose has a red trope that belongs to the class of red tropes. And when we say that red is a color, we mean that the class of all tropes of red (universal-r) is included in the class of all tropes of color (universal-c).
   However, there are problems with this view. First, there is a problem with the notion of class. If a class is seen as an abstract object, it seems that we are abandoning the great advantage of trope theory. And there is a problem with size: a class can become larger or smaller; but a universal cannot change its size, for it has no size. Third, we can develop objections of regress concerning precise similarities based on Russell’s criticism of Berkeley’s and Hume’s nominalism. According to Russell, two patches of the same color have a relation of color-likeness that seems to be a universal or abstract idea… It is true that a nominalist can decide to consider applying the same analysis to color-likeness, considering it a particular. But then he will face the following problem:

We may take a standard particular case of colour-likeness, and say that anything else is to be called a colour-likeness if it is exactly like our standard case. It is obvious, however, that such a process leads to an endless regress: we explain the likeness of two terms as consisting in the likeness which their likeness bears to the likeness of two other terms, and such a regress is plainly vicious. (Russell 1994: 111-112)

To offer a more detailed explanation, we begin by assuming that likenesses or strict similarities are tropes, and that (using ‘=’ to abbreviate ‘strict similarity’) we have the tropes T1 = T2, T2 = T3, T3 = T4, etc. It must be what I prefer to call ‘strict similarity’ because mere similarity or resemblance lacks transitivity. If T1 is only similar to T2 and T2 is only similar to T3, then it is possible that T3 isn’t similar to T1. The solution is to appeal to strict similarity understood as a transitive concept and meaning the same as qualitative identity, which is the identity between different things (differing from numerical identity as the identity of the thing with itself). Qualitative identity does not need to be perfect: our cars are both yellow, but your car’s finish is faded. But the differences must have a limit. Corrigible differences are usually found within the range of a concept (e.g., turquoise blue and cobalt blue are both called blue) as far as we have a criterion of correction (say, wavelengths between 450 and 495 nanometers).
   Now, in order to construct the class of similar tropes, we need to know that the first trope of identity is like the second trope of identity. But how do we know this? Well, since it cannot be by appealing to the abstract idea of identity, it must be by appealing to a trope of qualitative or strict identity. Since the same question can be posed regarding the strict similarities between these strictly similar tropes, it seems clear that we are becoming bogged down in a kind of pyramidal infinite regress.
   Russell considered this regress as plainly vicious. Even if this is not the case, such a multiplication of tropes of likeness or strict similarities seems overwhelming to our finite intellects. I believe, however, that we are able to easily overcome this difficulty, inspired by just the kind of treatment that particularist philosophers like Berkeley and Hume gave to ideas or impressions in order to ensure their unity. According to this view, the universal could be defined as:

Universal (Df) = Any trope T* taken as a standard/model or any further trope that is strictly similar to T*.

Explaining this definition, we must remark that trope T* used as the standard doesn’t need to be always the same. On the contrary: one can choose any trope strictly similar to T* and use it as T* in order to make comparisons. Moreover, what we normally know of T* is some recollection in our memory.[5]
   Accepting this definition, we do not need to take recourse to sets of similar tropes or even to a mereological sum in order to explain universality, since the definiens covers any trope strictly similar to T*. The problem of size disappears, since for the definition it is not a question of how many tropes are identical to T*. When a person utters the sentence ‘This rose is red,’ she means that this rose has a trope of red Tr1 that is identical to a trope of red Tr*, taken as a standard, as retained in the person’s memory. When she utters the sentence, ‘Red is a color,’ she means that some Tr1* is also a Tc (color-trope), and that each trope strictly similar to Tr* is also a Tc by being in a looser way also strictly similar to Tc* as the wider paradigm of a color trope. Finally, Russell’s problem also disappears, since we don’t need to compare one identity with the other, but only the tropes ‘T1, T2… Tn’ individually with trope T*. Instead of possibly generating an infinite pyramidal regress, the schema will take the form ‘T1 = T*, T2 = T*… Tn = T*’. In other words, as long as the chosen standard trope T* remains one and the same, there is no need to compare similarities with similarities, in this way reaching similarities of similarities. Russell’s problem would not arise because our definition makes the universals potentialities instead of actualities.
   Furthermore, we can also construct the universal ‘strict similarity’ requiring that some trope Ts* (trope of strict similarity) is taken as a standard and allowing it to be compared with any other trope of strict similarity strictly similar to Ts*. Our schema will be: ‘Ts1 = Ts*, Ts2 = Ts*… Tsn = Ts*’, where Ts* can always remain one and the same. This means that we have second-order strict similarity tropes referred to by the strict similarity signs between Ts1 and Ts*, between Ts2 and Ts*, and so on – call them Tss1, Tss2, etc. So, in order to make reference to the universal composed of these strict similarities of strict similarities, we need to appeal to a standard trope of strict similarity of strict similarity Tss*, and it is easy to predict that we can refer to an infinite number of higher-order strict similarity tropes in this way.
   Would be this a vicious regress? I don’t think so. For nothing prevents us from stopping where we wish, insofar as we see no reason for going further – a point that is to be understood in terms of explanatory demand. If we do not see any explanatory advantage in going further, we can simply stop where we choose to. A similar consequence results from Platonic realism. As H. H. Price noted (1953, ch. 1): the idea of the ideas constantly used in Plato’s doctrine of ideas is a second-order idea. But Plato stops with the idea of ideas simply because there is no explanatory advantage in going further, considering, for instance, the idea of the idea of the idea. In the same way, we can find no explanatory advantage in going beyond precise similarities between first-order tropes.
   Finally, it is worth noting that strict similarity is not a trope like others. To begin with, it is what one could call a dependent trope: it depends on the existence of things considered to be alike; color-likeness, for instance, is an internal relation depending on the existence of colors. Campbell suggested that strict similarity is only a supervenient pseudo-addition that does not add any being to what alreay exists (1990: 37). But the fact of being an internal relation does not make strict similarity a quasi-trope or a non-trope, considering our identifying condition of tropes. There are reasons to countenance its reality as a trope, even if distinguishing strict similarity from other more concrete kinds of tropes. First, the condition for the existence of a (simple or complex) trope is its spatio-temporal location, established by the application of its denoting predicative expression. We can argue that similarity is also spatio-temporal, though in a broad way. For example: when I consider the strict similarity between the colors of two shoes I am looking at in a store window, the likeness would be somewhere in this place, which may include myself, but not in a distant place. My home and the Taj Mahal have a color-likeness: both are white. But I can swear that this likeness is situated on the planet Earth and not on the surface of the sun. Moreover, if my home or the Taj Mahal is destroyed, the color likeness also disappears, which means that it also exists in time. On the other hand, when someone considers similarities between the form of our Milky Way galaxy and the form of the Andromeda galaxy, this coarse grained qualitative identity must have to do with the total distance between them, which is still located, and as great as it may be, is ridiculously minuscule compared with the immensity of the cosmos.
   The problems for the theory of tropes do not stop here. What about other relations? For example, the Golden Gate Bridge is (on the average) 67 m. above sea level. Surely, this spatial relation is there and can even be measured. And this relation is located in space and time, enduring as long as the bridge exists. Even if this spatial relation is internal, depending on the existence of its relata, it can be classified as a trope, since it satisfies our identifying condition for tropes of being spatio-temporally localizable.
   But what about space and time in themselves? Normally we admit that all that exist are tropes and space-time. Even in realist ontologies a separate existence of space and time was never questioned. However, could space-time be in some way tropes or something derived from tropes? Imagine that all objects and properties of the world disappear. Would space (and time) remain? I believe that we have the intuitive tendency to answer in the negative. However, according to Newton’s theory of absolute time and space, the answer was in the affirmative: space and time were seen as individual-like entities. Space would be like a great container with material objects within it and would not cease to exist even if all the matter disappeared. On the other hand, according to the relational view defended by Leibniz, space could be constructed by means of relations, which can easily be extended to time. In this case, space and time could not exist in themselves, because by being constructed of relations they demand the existence of material objects (Alexander 1956). Both answers have always been controversial, and the discussion has become even more complicated due to the theories and discoveries of contemporary physics.
   Anyway, aside from the Newtonian view, it seems that there is some possibility that we can explain space and time in terms of tropes. In a unsophisticated commonsensical approach, we could to define space relationally, possibly beginning with relations like above, under, in front of, behind; e.g. ‘object x is located twice behind object y in relation to z’. Time could be defined relationally, by means of relations like earlier, simultaneous, later; e.g. ‘event x occurs three times later that event y in relation to event z’… And we could use regularities as parameters: a foot to measure distances in feet, a day to measure periods of days… However, since tropes are seen as spatio-temporally localized entities, it seems that we would end in circularity: space and time would be defined as relations of spatio-temporally located properties.
   The answer to the circularity objection in this very modest commonsensical approach could be that space is constituted by a network of relations among entities that can be quantitatively compared. For instance, consider the following rough description of the Southern Cross: star c is below b and twice as distant as b is from a, while stars d and c are on opposite sides of b and the same distance from b as a is from b. With this approach, any particular spatial relation could be located in the spatial network and because of this be defined as a trope. Likewise, we could locate the terms of these relations as tropes or clusters of tropes (the same for time-relations like before, simultaneous and after). However, it is an entirely open question whether such rough intuitive views could be developed and extended in order to comprehend the sophisticated theories of contemporary physics and their distinct domains.

3. Tropes and Concrete Particulars
The second major problem is that of constructing concrete particulars by means of tropes. For D. C. Williams, a concrete particular is a bundle of tropes (1953: 7 f.). Tropes are spatio-temporally conjoined to form concrete objects. The advantage of this view is that it enables us to abandon the old and obscure concept of substance understood as a hidden substratum of properties. For the trope theorist, the concrete particular turns out to be like an artichoke, which consists only of its leaves, which are the tropes.
   The key-concept here is that of compresence (also called concurrence, togetherness, etc.), which can be understood as the sameness or quasi-sameness of the spatio-temporal location of tropes. We can analyze the concept of compresence as composed of two other concepts: co-location and co-temporality. The co-location of tropes is their joint location in a certain region of space, leaving aside when each of them is placed in this region. Thus, two persons who take turns sleeping in the same bed can be said to be co-located in this place. The co-temporality of tropes is their simultaneous existence during the same time-interval. Thus, my friend Magda and I are co-temporal, though not co-located, since we are very distant. The compresence of tropes arises only when they are co-located and co-existent.
   A naïve but instructive objection to the view according to which concrete objects are bundles of tropes is that if it is true, then all predication turns out to be tautological: the utterance ‘This chair is yellow’ would be tautological, because yellow is predicated of a subject that already has the trope yellow as a constituent (Loux 1998: 103). This objection is easy to refute. All we need is to distinguish necessary from contingent tropes. The necessary tropes are those typically specified in a definition. A chair is defined as a seat with a backrest, designed to be occupied by only one person at a time. The seat is a sub-cluster of tropes, the backrest another, and the fact that this object is designed to be used by only one person is a dispositional sequence of tropes that completes the definition. There are also contingent tropes, like those constituting the sub-clusters of armrests or four legs (there are chairs without armrests or four legs). And there are still more casual tropes associated with a chair, like its color, the relation of a person sitting on it, its distance from a table… The concept of a chair is one of an artefact. But we can consider natural kinds in a not very dissimilar way. Gold is defined as an element with the atomic number 79, being a yellow, dense, and precious metal. But its having a determined atomic number is a necessary trope, though gold does not need to be yellow or dense or even a precious metal, since these are contingent tropes.
   Peter Simons gave what seems the best answer to this question by suggesting that a material object should not be seen as an unstructured cluster of compresent tropes. It is typically made up of a nuclear kernel of necessary tropes giving a foundation to an accidental halo of contingent tropes. The halo-tropes can be replaced by tropes of other kinds, but the kernel-tropes cannot. Consequently, the halo-tropes can be said to be specifically founded on the kernel-tropes, while the kernel-tropes only generally found the halo-tropes (Simons 1994: 376 f.). Simons admits the possibility of a concrete object formed only by kernel-tropes, etc. A precise definition is difficult if not impossible. A stone is a material object that can be composed by very different materials having few things to individualize it except compresence and a tight connection of form, hardness, solidity, weight, volume, colors... among its tropes. But based on this bunch of properties, we can re-identify the stone as the same one.
   Unhelpfully, compresence and kernel-tropes are still not enough to define material particulars. Socrates’ wisdom is a dispositional property consisting in a complex and varied trope, as it seems. These tropes have compresence, since they are located where Socrates is. Moreover, they can have a kernel: the ‘peculiar Socratic core of wisdom’. But they are not a material object, not even an individual, since in principle others could share strictly similar qualities of wisdom. A common rainbow is constituted by co-located and co-temporal tropes of colors and forms – the seven colors of the spectrum – as its core, but it is less than a material object. The holographic projection of a teacup also has a compresent set of colors and forms. They belong to its core. But despite having colors, spatial extension and form, it is no material object!
   One strategy to deal with this problem is to add to the core of compresent tropes some tropes that seem to be necessary for the identification of our usual material objects. They are: volume, form, some degree of hardness or solidity (measured by resistance to pressure), some weight (related to presence in a gravitational field) and the possibility to be moved, all related by compresence. This already excludes Socratic wisdom, the rainbow and the holomorphic projection. But liquids, though material objects, do not have a specific form or solidity, unlike a stone, a tree, a table. For example, water takes the form of its container, and more water can be added to an amount of water, changing the volume. In a frozen state or as water vapor it ceases to be liquid.
   Resistance to pressure can be lower or higher. The water in a glass is material, though not properly a material object, since it lacks a definite form, and it can resist pressure. A cloud has a low level of materiality, but even so its droplets have some minimal resistance to pressure. But what about material objects like viruses or atoms or electrons and the hypothetical strings in string theory?
   My proposed answer is based upon the assumption that our commitment to commonsense does not exclude science. We can refine our idea of hardness or resistance to pressure by proposing that a necessary trope constitutive of the core of any physical object is a derived trope called in physics mass. In physics the mass of a material body is broadly defined as its resistance to acceleration when a force is applied (as far as I know, this idea is accepted in both Newton’s and Einstein’s mechanics).[6]
   We conclude that having mass, some size, mobility and compresence of its central tropes seems to be necessary for identifying the core of a material object and perhaps of any physical object. This excludes electromagnetic, gravitational, weak and strong forces, which are better seen as tropes. But this result cannot be generalized to any individual. Consider individuals as a crowd or the British Empire. These individuals do not form a physical object. Different from material objects, a crowd and the British Empire are composed of tropes that are supervenient to material, not tightly connect physical entities.
   Another difficulty arises from the alleged fact that the idea that particulars are clusters of tropes is vulnerable to a regression argument parallel to the third man argument used against the abstract objects assumed by a Platonist ontological view. Thus, suppose that a concrete particular were constituted only by the tropes T1, T2, and T3. Since the relation of concurrence could not be an abstract entity, it must be a trope. Call this relation Tc. In this case it seems that we need a new concurrence for T1, T2, T3 and Tc, which will be Tc’, and so on infinitely (Daily 1997: 158).
   My proposal against this objection takes a form similar to what realist philosophers have applied in defense of their own abstract properties. Compresence is made up of co-location plus co-temporality, which are spatio-temporal delimitations that remind us of the cases of form and duration. They are sui generis tropes, since they behave somewhat like Platonic ideas with their resistance to self-predication. In other words: although you can meaningfully say that this red is red, and even that that triangle is triangular, you cannot meaningfully say that a concurrence is concurrent (or even that a co-location is co-located or that a co-temporality is co-temporal or even that the identity is identical). Concurrence is a sui generis non-self-predicating limiting trope, requiring no new trope of concurrence to warrant its own co-location and co-temporality together with other tropes. Also the strict similarity is a sui generis trope, because one cannot say of the strict similarity between T1 and T2 that it is strictly similar, for this would make no sense.
   As I have shown, not all individuals are material objects. Social entities like the British Parliament and historical entities like the Battle of Hastings are in themselves not material objects. They are complex structures made of tropes, mental tropes like intentional states and depend on material entities to be spatio-temporally located, even if only in a vague way. Since these tropes are unique and identified by nominal terms, they are particulars.
   What to say about individuals that are formal entities like numbers? They seen not to be made up of tropes, since they are non-spatio-temporal. However, I have my doubts. The empirical world is made up of quantities. Would the number 3 exist if the world didn’t exist? Although this is a queer question, the tendency is to answer in the negative. Perhaps numbers are only a compact way to speak of the numerals used to count empirical objects. We learn numbers by counting material objects: ‘There are three apples and two pears in the basket, totalizing five fruits’. In this case, the ascription rule of the predicate ‘…is a fruit’ has shown its effective applicability to five spatially distinct objects, attributing physical existence to all of them. In this case, the attribution of the number five seems to be the a higher-order property of the ascription rule extracted of its being effectively applicable to each one of the distinct fruits in the basket until the attribution of existence to them all.[7] But what about the number five in itself, abstracted from its application in counting objects, as it is used in pure mathematics? Is this an abstract object like a universal? Or is this also a Platonist illusion? Isn’t it also here only a disjunction between a model of a higher-order property of having five distinct higher-order effective applicabilities of the same rule (five existences) and any precisely similar case of the higher-properties of effective applicabilities? In the positive case, it could be suggested that even the abstract world of mathematics is built up of some sorts of thin higher-order tropes situated at the peak of a building whose genetic-epistemic foundations are our well-known sensorally given quality-tropes, si that numerical tropes are also dispersed around the world and able to be meta-predicatively designated. These are, of course, only speculative divagations! But they serve to give us an idea of the instigating problems that a developed trope theory would have to face.
   Much of what I have written here is speculative, demanding a great deal of work and refinement. I could not do more than to offer a sketch of what seems to me clearly the most plausible way to deal with a category that will play a central role later in this book.








[1] This ground-breaking work was D. C. Williams’ paper ‘The Elements of Being,’ published in the Review of Metaphysics (1953); he was the first to propose constructing the whole world using only tropes as building-blocks. An important attempt at a systematic development of the theory was Keith Campbell’s book, Abstract Particulars (1990). Since then, the discussion devoted to this problematic has steadily grown. For access to the literature, see Anna-Sofia Maurin’s 2013 article in the Stanford Encyclopedia of Philosophy.
[2][2] In his book on tropes, Campbell writes: ‘because boundaries in space need to be drawn rather than revealed it is perhaps best to view individual specimens of each of the shapes as quasi-tropes rather than as genuine tropes’. (1990: 91) This argument is not very convincing, since the conventionally charged intromission of the epistemic subject is inevitable in any conceptual application.
[3] The objection is based on Bradley’s proof that reality is an indivisible unity, because there can be no ontologically real relations.
[4]  I have heard that in Russian there is no proper verb for the copula. Russians say something like ‘Me beautiful’, ‘Me good’… This seems to reinforce the idea of its really pseudo-additional character.
[5] We can imagine circumstances in which people are unable to retain memories of the color trope T, but bring with them templates with patterns T* of this color trope, comparing these patterns with any found trope and calling the possible effects of this hability the universal of this color.
[6] As it is well-known, the reason why according to relativity theory a body cannot reach the speed of light is that at this speed its mass would become infinite, requiring infinite force to accelerate it.
[7] See the discussion of existence in chapter 4, sec. 11-17.



quinta-feira, 24 de novembro de 2016

MODAL ILLUSIONS: AGAINST TRANSEPISTEMIC METAPHYSICAL IDENTITIES (Kripke et caterva)

Obs: this is an uncorrected draft for the book Philosophical Semantics, to be published in 2017 by Cambridge Scholars Publishing.





Appendix to Chapter 2


MODAL ILUSIONS:
 AGAINST TRANSEPISTEMIC METAPHYSICAL IDENTITIES



Die Probleme, die durch ein Mißdeuten unserer Sprachformen entstehen, haben den Charakter der Tiefe. Es sind tiefe Beunruhigungen; sie wurzeln so tief in uns wie die Formen unserer Sprache, und ihre Bedeutung ist so groß wie die Wichtigkeit unserer Sprache.
[The problems arising through a misinterpretation of our forms of language have the character of depth. They are deep disquietudes; their roots are as deep in us as the forms of our language and their significance is as great as the importance of our language.]
Wittgenstein

Although exceedingly original and challenging, Saul Kripke’s philosophical application of modal logic to the problems of reference seems to me to be burdened by a disturbing web of confusion. Since many disagree, I will try to justify myself through a critical discussion of his article ‘Identity and Necessity’ (Kripke 1971), which precedes the more developed views defended in his book Naming and Necessity (Kripke 1980), since that short article takes some fundamental ideas direct from the oven. Paragraphs summarising Kripke’s article are printed in italics to be distinguished from paragraphs containing my own comments. To my coments on this article I will in the addendum make some short criticisms to some central views not only from Kripke, but also from Hilary Putnam, Gareth Evans, David Kaplan, Tyler Burge and John Perry, as part of my project of debunking the metaphysics of meaning.

Kripke begins by considering the modal argument for the necessity of statements of identity. Where is the operator of necessity, which here will be seen as de re (regardless of the mode of linguistic designation), we can consider that, given the principle of indiscernibility of identicals, according to which ‘(x) (y) ((x = y) → (Fx → Fy))’, and given the principle of identity, according to which ‘(x) (x = x)’, we can conclude that if the property F is to be necessarily applied to x, then y must also have this property, i.e. it is necessary that y equals x; in symbolic notation, (x) (y) (x = y) → ((x = x) → (x = y))’, namely: ‘(x) (y) (x = y) → (x = y)’.
   This apparently inconsequential formal result leads Kripke to the bold conclusion that, as long as there are theoretical (essential) identities, identities between names are necessary. We know that by universal instantiation ‘□(x = y) → □ (a = b)’. That is, if a and b are real names and ‘a = b’ is a true identity, then this identity is necessarily true. This would concern identities like ‘Hesperus is (the same as) Phosphorus’ and ‘Cicero is (the same as) Tulius’: they must be necessary. Further, if F and G are theoretical predicates, defined as essential designators of properties, if they form a true theoretical identity of the form (x) (Fx = Gx), then this identity is also necessarily true. That is why identities like ‘Heat is molecular motion’ and ‘A state of mind is a physical state’, if true, are necessary.
   Kripke recognises that identities between names and theoretical identities have generally been considered contingent, and presents the reasons for it. Consider the statement ‘Hesperus is Phosphorus’. Since Hesperus is Venus seen at dusk (evening star), and Phosphorus is Venus seen at dawn (morning star), it was an important astronomical discovery that they are actually the same planet, as Frege has noted. Therefore, this seems not to be a necessary, but rather a contingent empirical truth. The same applies to theoretical identities such as ‘Heat is molecular motion’. This identity was a discovery of science and could be false, because if caloric theory (the theory that heat consists of a self-repellent fluid called caloric) were correct, heat wouldn’t be molecular motion. This seems to be a clearly contingent statement, since it could be otherwise.
   Kripke’s thesis, however, is that contrary to the appearances, all these identities, despite having been learned a posteriori, are necessary, even if they do not seem to be. To reinforce his thesis he introduces an important distinction between the rigid designator, here defined as a term that refers to the same object in all possible worlds in which this object exists ou would exist, and the non-rigid or accidental designator, which can refer to different objects in distinct possible worlds. Proper names and terms of natural species, at least, are rigid designators, while definite descriptions are accidental designators. Hence, if we have an identity in which the identity symbol is flanked by proper names, this identity is necessarily true if true at all, considering that proper names cannot change their reference in different possible worlds.

It seems clear that a mathematical term can be seen as a rigid designator, insofar as it does not depend on how the world is; but could our empirical proper names not be rigid designators? In the attempt to show that they could be accidental designators, we can imagine that it were discovered that after the childhood of G. W. Bush an extra-terrestrial creature possessed his body, and since then has lived in it and maintained his identity, becoming in this way the president of the United States and performing all actions attributed to him. Would not in this case the proper name ‘G. W. Bush’ be used to refer to this extra-terrestrial creature instead of the son of Barbara and George Bush, being im this way an accidental designator?
   I think that the idea that the proper name is a rigid designator would resist to this objection. According to Kripke’s views, the reference of a proper name is determined by an act of baptism, so that the true W. G. Bush, a rigid designator, would have since long disappeared. On the other hand, a homonymous being, the embodied extraterrestrial being, whose true name is Gkw9, would have had in some remote day a baptism and the name W. G. Bush, as a nickname of Gkw9, would apply to the same extraterrestrial being in each possible world where it would exist, being therefore also a rigid designator.
   Nonetheless, applying my own theory of proper names summarized in the appendix of chapter 1, the results would be the same. According to this theory the referent of a proper name is the object that satisfies the identifying rule for the application of the proper name. And what this identifying rule requires is a sufficient and better than any other satisfaction of the disjunction of the fundamental description-rules, which are the localizing and the characterizing rules. For the adult W. G. Bush (Gkw9), for instance, the localizing description includes his spatio-temporal career in the planet Omega before his embodiment and on the Earth after its Bush-embodiment, while the characterizing description would include his deeds, as his election as the 43tr president from USA, the wars in Irak and Afganistan, and the person who earlier in the planet Ômega has make the deeds of Gkw9... In every possible world were this identifying rule is satisfied, W. G. Bush (Gkw9) would exist. Hence, the identifying rule for the name is a rigid designator for us too. Something of the kind could be easily established for the child named W. G. Bush, the true Bush, making this name also a rigid designator.
   Something different, however, is the idea that the concept of rigid designator has the consequences that Kripke expected as a way to ensure existence of de re metaphysical necessities of identities between our usual proper names and between terms of natural species.
   Kripke believes to have warranted the necessity of this identity by having discovered some radical difference of nature between proper names, on the one hand, and definite descriptions, on the other. What his words suggest is that a proper name would reach its reference without intermediaries by means of a direct (in my view purely magic) relation instaured in the act of baptism, which does not really depend on any property of the object, allowing then the production of external causal chains that in the end would reach each speaker of the name who really refers to its bearer.[1] A definite description, on the other hand, is only an accidental designator: it would refer to different objects in different possible worlds, probably because it has what Stuart Mill called ‘conotation’, which is its implication of an attribute that the object may have (1881, I, ch. 2). Using Kripke’s example, this would be the case of the description ‘the inventor of the bifocals’, a description who refers to Benjamin Franklin in our world, but that could refer to any other person and even have no reference in a different possible world.
   I think that this strange dichotomy, suggesting a mysterious difference in the nature of reference is totally dispensable if we apply my own neodescriptivist theory of proper names, since this theory gives a perfectly reasonable explanation for the rigidity of proper names versus the accidentality of definite descriptions (see appendix of chapter 1). Following this last theory, I agree with the idea that the necessity of the rigid designator is always de dicto, supporting John Searle’s view according to which the de re necessity is only a sub-class of the de dicto necessity, without any metaphysical import (Searle 1983: 208-220).
   The neodescriptivism I propose makes a proper name a rigid designator because any combination of descriptions that allows its reference in accordance with its identifying rule must be satisfied in any world in which the proper name has a bearer, simply because the identifying rule define what its bearer can be. However, two different proper names of the same object can have different identifying rules, identifying their bearer under different guises, under different ways of presentation, simply because they amphazise different perspectives in which different descriptions or groups of descriptions are satisfied. In this case, even being rigid designators, we cannot a priori know that they are referring to the same object, and it may be an empirical matter to decide if two different rigid designators are referring to the same object or to two different objects. We still do not know whether the identifying rules of the two names are part of a common identifying rule, being the identitity sentence at this first stage contingent a posteriori. This state of affairs endures until after empirical experience we establish by convention that the different ways of presentation, the different identifying rules, are constituents of the same rigid designator, building in this way a more complex identifying rule that includes both, each of them emphazising a different perspective. But in this case the identity will be necessary a priori! In no moment of this process, however, we need to resort to a Kripkian necessary a posteriori identity.
   Only to illustrate the point: there is a way to express Frege’s insight according to which ‘Afla = Ateb’, in which Afla is the same mountain as Ateb, though explored from a different complementary perspective, what gives to these names different but complementary senses or modes of presentation. Since for Frege references are dependent on senses, the proper names ‘Afla’ and ‘Ateb’ are from the beginning de dicto rigid designators and not metaphysically de re rigid designators. However, some day the explorers can ask themselves whether Afla is Ateb. At first they see this identification as a contingent matter. After they discover that they are indeed referring to the same mountain, the more complete identity sentence turns to be seem as having the implicit form ‘Afla [-Ateb] = Ateb [-Afla]’, that is: Afla and Ateb express rules identifying numerically the same object simply because they turned can now be blended in the formation of one and the same identifying rule, applicable to both sides of the the same mountain, though under different guises.

Kripke also considers the problem of apriority. A priori truths are those that we can know without appealing to experience. Many consider the necessary and the a priori to be equivalent. But the concept of necessity is according to him metaphysical about how the world must be – while the concept of a priori is epistemic – about how we know the world. Kripke thinks that the two classes are not equivalent. Consider, he writes, Goldbach’s conjecture, which states that any natural number above two is the sum of two primes. It may be a necessary truth without the possibility of our knowing it a priori. In this case it would have metaphysical necessity.

The suggestion that necessity is metaphysical while apriority is epistemological is highly questionable. This distinction would be justified only if there were metaphysical de re necessities, as Kripke intends, since a de dicto necessity would follow from a seemingly trivial epistemologic apriority, even if well grounded. However, the existence of metaphysical de re necessities in the supposed sense seems to be something that escapes our cognitive faculties, since our empirical knowledge is inherently fallible, something that has been insistently repeated by philosophers of science from C. S. Peirce (1991, ch. 7) to Karl Popper (1959). All that we can do is to postulate empirical necessities by accepting the most well-entrenched[2] and strongly inductively grounded regularities as natural laws (Tugendhat 1983; Mackie 1974). To really know if there is a necessity of a natural law beyond this well-grounded postulation (pace Armstrong) would require absolute knowledge – something that our epistemic falibility makes impossible. Therefore, the necessities of natural laws are nothing but a result of a well-grounded decision to treat them as necessities. They are necessities in a weaker sense of the word; however, once postulated by us as natural laws they turn to be treated as basic rules of our conceptual system.
   Thus, if our analysis of necessity is correct there seems to be two kinds of necessity, both of them epistemic: (i) the logical or conventional necessity that we find in definitory sentences (like ‘brothers are persons with the same parents’) or in formal sciences (like ‘~(A & ~A)); (ii) the empirical necessity, which is reached a posteriori, but afterwards can be simply postulated as necessary, as far as it is useful and it is useful to work with them in this way.
   Wittgenstein would classify empirical necessities as ‘grammatical rules’ – rules grounding a useful linguistic practice (Wittgenstein 1984a). Here is his suggestion, in which we read the word ‘rule’ involving a priori propositions:

Every empirical proposition can serve as a rule if it is fixed as the unmovable part of a mechanism, in such a way that the entire representation revolves around it, making it part of a system of coordinates independent of the facts. (Wittgenstein 1984e, part VII: 437)[3]

To illustrate what this can mean, consider the statement of some particular physical law, for instance, Einstein’s famous ‘e = mc2.’ It can be doubly understood:

(a)  As a component of the special theory of relativity, under the assumption of the truth of this theory. – In this case, it will be seen as necessary a priori, that is, as a kind of postulate independent of experience: its necessity is conventionally postulated (we could say with Wittgenstein that the statement is hardened, becoming an inmovable part of a mechanism).
(b)      As a mere element of our ever possibly changeable overall system of beliefs. – Hier, however, the same physical statement should be considered as an a posteriori contingent statement. After all, in principle it could be always falsified by observation, assuming that fallibility is a pervasive trait of our empirical knowledge (with Wittgenstein we would say that the truth of the statement is treated as fluid, remaining dependent of the way the world is).

Attention to this two ways of considering a statement can lead us to suggest that the statement (i) ‘Heat is molecular motion’ can be read in two ways:

(a)  As a necessary a priori statement – if read as a piece of the subsystem of beliefs that constitutes the thermodynamics under the assumption of the truth of this subsystem. In this case (i) means (ii): ‘(Necessarily and without considering the experience) heat in gazes is molecular motion [under the assumption of the truth of the thermodynamics]’.

So it is read after the general acceptance of the the kinetic theory of gases. But for chemicists still in the second half of the XIX century this was still a discovery and could be read as:

(b)  A contingent a posteriori statement, if understood in its relation to our unstable overall system of beliefs. In this case (i) means (iii): ‘(Contingently and in the dependency of experience) heat in gazes is molecular motion [according to what we have found out of experience until now]’.

Consider now the first example from Kripke: (iv) ‘Hesperus is Phosphorus’. According with the suggested analysis it can be read as:

(a)  A necessary a priori identity statement – if it is read as a piece of the subsystem of beliefs that constitutes our astronomic knowledge under the assumption of the truth of this subsystem.  In this case (iv) means (v): ‘(Necessarily out of the experience) Hesperus = Phosphorus [under the assumption of the truth of our present astronomical knowledge]’.

So it is today. But as the Babylonian astronomers first figured out that Hesperus is Phosphorus, by considering its size and by noticing that both stars tracked the sun… in this case they read (iv) as:

(b) A contingent a posteriori statement, understood in its relation to our unstable overall system of beliefs. In this case (iv) means (vi): ‘(Contingently, under the dependence of experience) Hesperus is Phosphorus [according to what we have found out of experience until now]’.

If this reasoning is correct, then it is easy to conclude that for Kripke the statements ‘Heat is molecular motion’ and ‘Hesperus is Phosphorus’ are necessary a posteriori simply because he is confusedly combining the necessity of the (a) reading of these statements with the aposteriority of their (b) readings.[4]
   As for Goldbach’s conjecture, the fact that it may be a necessary truth without our being aware of it does not mean that its necessity isn’t a priori or has some indefinite status. It is not impossible that someone finds a proof of this conjecture, giving to it the status of a theorem with a priori necessity. Moreover, it is because the mathematicians hold as a heuristic rule that it is possible to reach such an a priory knowledge that they insist in searching for a proof; otherwise they would not sustain the conjecture.

Maybe the most stricking example of a necessary a posteriori statement introduced by Kripke is that of the wooden table in front of him. It starts with the question: could it have consisted since the beginning of its existence of ice from the Thames? Certainly not: It would be a different object. Thus, the statement ‘This table, if it exists, cannot be made of ice,’ is a necessary truth known a posteriori. Tables, he says, are usually not made of ice. This table seems to be made of wood, and it is not cold. Hence, it is probably not made of ice. Of course, this could be a delusion. It could actually be made of ice. But that’s not the point, says Kripke. The point is that given the fact that the table is not made of ice, but of wood, one cannot imagine that it could be made of ice. Given the fact that it is not made of ice, he concludes, it is necessary that it is not made of ice. In other words: being P = ‘This table is not made of ice’ we know a priori the truth of ‘If P then P’. Moreover, he says, we know from empirical research that P is true. Combining these two statements, he constructs the following argument applying a modus ponens:

        (A)
     1 P □P
     2 P
     3 □P

It is therefore necessary that the table is not made of ice, although this is only known a posteriori, by empirical research. The statement; ‘This table is not made of ice’ is necessary a posteriori.

The covert mistake in Kripke’s argument concerns the epistemological status of P in the second premise. In this premise the truth of P is affirmed in the desconsideration of the fact (earlier confusively refered by Kripke) that P, as any empirical statement, can only be known as true by inevitably fallible epistemic subjects. But if it is so P can in principle be false. Hence, the statement P of the second premise should be more precisely written as (2’): ‘It is practically certain that P (that this table isn’t made of ice)’, and I understand a statement as practically certain when it is extremely likely to be true, that is, when we can assign to its truth a probability very near to 1 (see Locke 2013).  Indeed, it must be so, because only God – the infallible and omniscient epistemic subject – could know with absolute certainty the truth of the statement P (that is, would be able to assign it the probability 1). God could know for sure the factual existence of P, in this way giving to the affirmation of P a truly metaphysically de re necessity. Unfortunately, we cannot appeal to God in this matters. Hence, all that we can know is that P is practically certain in the already pointed sense of being, under the assumption of all our present body of information, extremely likely to be true. This must be so, since our empirical knowledge is never absolute (it is always possible, for instance, that for some reason I believe I am standing before a hard wooden table, although it is actually made of ice, as Kripke himself admits).
   Assuming this, consider now the first premise. The same cannot be said of it, since it is a conditional. It is fully acceptable that given the fact that P – or, more precisely, if the fact that P is really given – then it follows that P is necessary. So, what P → P says is (1) ‘If it is really the case that P, then it is necessary that P,’ and this, I concede, is a logical truth. But what the antecedent requires is that P implies □P only if the truth of P is absolutely certain, for instance, knowable by God’s omniscience. Hence, the most complete analysis of premise (1) would be (1’): ‘If it is absolutely certain that P is the case (if P has the probability 1), then it is necessary that P’, but surely not as (1’’) ‘If it is practically certain that P is the case (that is, if P has a probability near to 1), then P is necessary’, for the mere probability of P, no matter how high, if less than 1, would not warrant the necessity of P. Admitting the changes of premise (1) to (1’) and (2) to (2’), Kripke’s argument can be made more explicit as saying:

     (B)
1’. If it is absolutely certain that P, then it is necessary that P.
2’. It is practically certain that P.
3’. It is necessary that P.

This argument is obviously non-valid, since the modus ponens cannot be applied to (1’) and (2’) in order to give us (3’). And the reason is that the antecedent of (1’) does not say precisely the same thing as (2’), what makes the argument equivocal, hence fallacious. We conclude that under a better scrutiny Kripke’s argument does nothing to convince us that we can know that the utterance ‘This table is not made of ice’ is a metaphysically necessary a posteriori truth.
   Now, the reason for Kripke’s misleading view that the conclusion of his own argument must be necessary a posteriori becomes evident. He ignores the fine semantic differences made explicit in the argument (B) and by doing so he jumps to a conclusion that unduly joins the necessity of the first premise of his argument with the aposteriority of its second premise, building what he calls a necessary a posteriori truth in the conclusion 3.

Kripke comes then to the analysis of identities between proper names such as ‘Hesperus is Phosphorus’ and ‘Cicero is Tulio.’ These are empirical identities, generally considered contingent. For Kripke they are identities between rigid designators, which make them necessary, since in the most diverse possible worlds these names will refer to the same object, a situation not possible where Hesperus isn’t Phosphorus or Cicero isn’t Tulio. We could, he says, have identified Hesperus and Phosphorus with two different celestial bodies, but in this case the sentence ‘Hesperus is Phosphorus’ would have a different meaning. This would be the case, for example, if Martians had once populated the Earth and had identified Hesperus with Venus and Phosphorus with Mars... The same is true with the identity ‘Cicero is Tulio.’ According to him it seems that this statement is contingent because sometimes we learn these names with the help of definite descriptions, like ‘the greatest Roman orator,’ which are accidental designators, thinking that we identify the object through properties, when in fact such names are not synonymous with descriptions, but rather with rigid designators.

One could produce here an argument parallel to the argument applied by Kripke to the indexical case of the table made of wood in the attempt to demonstrate the metaphysical necessity that Hesperus is the same as Phosphorus, since these names are rigid designators that must pick up necessarily the same object in any possible world. Calling Hesperus h and Phosphorus p we can build up the following Kripkian argument:

     (h = p) → (h = p)
     h = p
     (h = p)

However, here too the modus ponens does not apply because although the first premise is true, the second premise would only be able to assure us the conclusion ‘(h = p)’ if it were able to give us an absolute assurance of the truth of ‘h = p’. But this is not the case. In order to get the absolute assurance that ‘h = p’ that enables us to reach the conclusion, this truth must be discovered, not by inevitably fallible human epistemic subjects, but only by God, the omniscient and infallible epistemic subject. Because of this, ‘h = p’ can here only be seen as an empirically achieved fallible conclusion, saying that it is practicaly certain (extremely probable) that ‘h = p’, which is still not the same as its absolute certainty. The following formulation demonstrates again the hidden failure of the argument:

       If it is absolutely certain (with probability 1) that h = p,
       then (h = p).
       It is practically certain (with probability near to 1) that h = p.
       (h = p)

Since the absolute certainty required by the identity of the second premise with the antecedent of the first is not available, the equivocity of the argument is clear. We cannot use the modus ponens to derive the a posteriori necessity of h = p. The statement ‘Hesperus is Phosphorus’ is in this interpretation contingent a posteriori. It cannot be metaphysically necessary because being this identity only highly probable it remains always possible that Hesperus isn’t Phosphorus: it does not belong to these two identifying rules that they are necessarily unified in a same convention. For instance: although extremely unlikely, it is logically possible that the gods have produced a great illusion of knowledge in the human minds, and that the planets are nothing more than a swarm of fireflies that every night assemble to decorate the celestial Vault. In this case, Hesperus would have a different location than Phosphorus when seen by the naked eye, but it would look identical to Phosphorus when viewed through a telescope – not because it is the same planet or a planet at all, but as a result of an unknown kind of witchery.
   The second example given by Kripke is very different and it would be misleading to confuse it with the example above. It concerns the utterance ‘Cicero is Tulio.’ Assuming my proposed theory of proper names, the localizing description for his identification is (shortly) ‘Born in Greece in 3.1.106 BC and died in Rom 7.12.43 BC.’ And the characterizing description is (shortly) ‘the greatest Roman orator, a politician, lawer and philosopher.’ His whole name was ‘Marcus Tullius Cicero.’ Since the proper name does not belong to the fundamental descriptions, but to the auxiliary ones (he could receive another name in a different possible world), Kripke is only relying on the fact that not all speakers know that Cicero and Tulio are parts of a same proper name as a point of convention in our actual world, assuming that they know who is the bearer of the fundamental descriptions implied by these parts of the whole name.
   As a consequence, the question is a trivial one, namely, whether the speaker knows an auxiliary convention. Hence, the right answer is that ‘Tulio is Cicero’ is necessary a priori as a linguistic definition, since the convention that the whole name is ‘Marcus Tullius Cicero’ is something a priori, as much as the convention that a triangle is a trilateral figure. Moreover, to say that the statement ‘Cicero is Tulio’ is a posteriori would be to confuse its belonging to a definition in our actual world – which is a question of being informed about conventions – with the possible names that the same reference could have received in different counterfactual situations, where Cicero would not have been also called Tullius by forming the proper name ‘Marcus Tullius Cicero’. But this is as trivial as to say that in a different possible world one could give a different name for a triangle instead of ‘triangle’.
The next of Kripke’s examples concerns the identity between kinds of things, as in the already discussed statement Heat is molecular movement. Many think that this expresses an a posteriori truth, because it is the result of empirical scientific research. But for Kripke this is a necessary a posteriori identity, because the heat (in gases) cannot be anything other than molecular kinetic energy. It may be, he says, that the Earth could at some time be inhabited by beings who feel cold where we feel heat and vice versa, so that for them heat would not be identical with molecular motion. But this would not be the case, since heat is understood as molecular motion as we feel it. For Kripke the terms heat and molecular motion are rigid designators, which make the identity between them unavoidable. For him the fact that molecular motion produces the sensation of heat is used to fix the reference, making the identity necessary; the illusion of contingency is due to the fact that we confuse this with the fact that our identification of molecular motion with the sensation of heat is contingent.

As it was already noted, having ways to translate rigidity in descriptive terms, as it was shown in Appendix to chapter 1, we can link the two ascription rules of heat in gases and kinetic molecular energy, building a unified ascription rule that has two different guises, namely, different but interchangeable criteria of identification. I will not furnish an analysis of this rule here, but only show how a reasoning similar to that applied to the identity of proper names can be applied. Thus, considering heat in gases and molecular movement as rigid designators that necessarily designate the same essence, we could build the following Kripkian argument calling H heat in gazes and M molecular motion:

     (x) ((Hx = Mx) → (Hx = Mx))
     (x) (Hx = Mx)
     (x) (Hx = Mx)

Obviously the same kind of difficulty returns. The first premise says only that if it is really the case that (x) (Hx = Mx), then it is necessarily the case that all heat is molecular motion, or, from an epistemic perspective, if it is absolutely certain that all heat in gases is molecular motion, then it is necessary that all heat in gases is molecular motion. However, as the identity expressed in the second premise is always concluded by fallible epistemic subjects, even if they have the best reasons to believe it to be true, whe should construct a paraphrase of the above argument that highlights the misconception:

    (x) If it is absolutely certain (with probability 1) that (Hx = Mx),
          then (Hx = Mx).
    (x) It is practically certain (with probability near to 1) that (Hx = Mx).
    (x) (Hx = Mx)

Here again the analysis shows an equivocal and consequently fallacious argument. Because the antecedent of the first premise is different from the second premise, we cannot apply the modus ponens and the conclusion does not follows. The result is that we cannot by this way conclude that the statement ‘Heath (in gazes) is the same as molecular cinetic energy’ is a necessary a posteriori truth. However, if Kripke were right, this conclusion should follow.

The last of Kripke’s examples should be the most important one. It is intended as a refutation of the type-type identity theory of the mind-body relation, according to which ‘Pain is (the same as) such and such a brain state’ would be a contingent a posteriori scientific discovery, yet to be made. But, writes Kripke, ‘pain’ and ‘such and such a brain state’ are here rigid designators, because they refer to essential properties. However, if that’s the case, the identity theorist is in trouble, because the identity needs to be necessary, which clashes frontally with the fact that whenever you feel pain you do have a pain, while no one is denying that it is possible to conceive that we have pain without having the corresponding brain states. For a religious philosopher like Kripke this makes identity theory improbable.
   
I find this argument puzzling. First, one can as a matter of fact feel pain without being in pain – this can be done, for instance, with hypnotized people. But even if we correct this saying that we cannot feel pain without having the qualitative state of feeling pain, while we can for instance have water without the qualitative state of watery liquid in the case of the identity ‘Water is H2O’ (see Kripke 1980: 146), all that it is shown here is an assimetry between the ways we know each flank of the identity sign. This can be well the case. But despite this Kripke didn’t have shown why this assimetry compromises the possibility of fixing a possible necessity of the identity under the supposition of his own theory of de re metaphysical identity. Hence, he hasn’t show anything that makes his conclusion forceful in his own terms.
   Aside from this point, the objection here is the same as in the previous examples: from a purely ontological point of view it is always possible that pain is necessarily the same thing as some sort of brain state. The problem is that only God, the omniscient knower, would be able to know this in an absolutely certain way. For epistemologically fallible subjects like us, this identity can be only (a) be seen from an overall epistemic perspective as a contingent a posteriori truth, since from this perspective ‘pain is such and such brain state’ is able to mirror the ontological reality only in a very probable way (as practical certainty, building a weaker epistemic necessity); (b) be made a grammatical postulate, which is a necessary a priori truth. A further difference comparing this example with the example of heat is that we still do not have any sufficiently developed neuroscientific theory able to show clearly this identity. The unified ascription rule is here only a hypothesis that identity theorists have posed, since the brain is still today a mysterious black-box.
   In my view in most cases Kripke confuses the a posteriori element of a contingent a posteriori discovery with the necessary element of something conventionally established as necessary a priori, what may lead us to believe in a mystical metaphysically de re grounded necessity a posteriori. In doing so, he assigns to an ontologically unknowable identity the same status of an epistemologically alleged identity. He thinks as if we could assert ontological (metaphysical) truths without regarding our epistemic capacities and their limits. He refuses to accept that we cannot ever separate completely the epistemic from the ontic. In doing so he denies a point that modern philosophers were already aware, namely, that we lack access to transepistemic truths.



Addendum
There is a varity of arguments from Kripke and other externalist philosophers that deserve an examination. In what follows I will be short, as a more careful examination would exceed the scope of this book.

1. There is a variety of supposed examples of necessary a posteriory truths later suggested by Kripke and others. Consider, for instance, the statement (i) ‘Cats are animals’ (Kripke 1980: 181-2). For Kripke this is a necessary statement, since we cannot conceive a cat that isn’t an animal; but this is something discovered a posteriori. My answer is that statement (i) can be interpreted in two ways. As a mere result of an inductive inference (i) should be clearly read as a contingent a posteriori statement. However, (i) can also be read as a necessary a priori statement under the assumption of the truth of our contemporary taxonomy, according to which the cat is classified as an organism belonging to the kingdom animalia.[5]

2. Another kind of necessary a posteriori later suggested by Kripke concerns the origin. For him rigidity makes true parenthood necessary. Consider the sentence ‘Ismael Lowenstein is the son of Abel and Berta Lowenstein.’ According to a Kripkian philosopher this statement would be necessary a posteriori because even if this is known a posteriori, a person with different parents, coming from a different ovulo and a different spermatozoid, would not be Ismael Lowenstein. (See Kripke 1980: 112 f.).[6] 
   However, suppose that the adult Ismael makes the shocking discovery that his parents are not his parents; there was a mistaken change of babies in the hospital where he was born and the DNA analysis has proved that he is instead the actual son of Amanda and Mario Belinzoni. Of course, this is no reason to think that Ismael ceases to be called Ismael. This is even written in his personal identity card. If asked, he could insist in answering that his name is Ismael Lowenstein, probably with the agreement of others.
   Anyway, concerning the main point, namely, the whole statement ‘Ismael is the son of Abel and Berta Lowenstein’, with concerns the question of parenthood, the conclusion may be ambiguous.[7] One could use as criterion of parenthood (i) those who have take care of the child and nurtured him with love until the adulthood, and in this case the statement ‘Ismael is the son of Abel and Berta Lowenstein’ will be seen as true, even if he is originated from one spermatozoid of Mario and one ovulo of Amanda. Under this understanding the statement ‘Ismael is the son of Abel and Berta Lowenstein’ is contingent a posteriori. Contingent because it could be false that they have take care and nurtured him; and a posteriori because it depends on experience to be learned.
   However, it is easy to imagine a situation like that suggested by Kripke. Suppose that we were in the Nazi Germany and that Abel Lowenstein were Jewish. Suppose that the Nazis have catched him. It is clear that for them the criterion of parenthood was genetic. In this case Ismael Lowenstein would be considered son of Mario and Amanda Belinzoni, while Carlos would be considered the son of Abel and Berta Lowenstein and sent to a concentration camp. Finally, it is even possible that the Nazis have established that the true name of a person must be related to her genetic origins, concluding that the person called Ismael Lowenstein is in fact Mario Belinzoni and that Mario Belinzoni is in fact Ismael Lowenstein. Anyway, even in this case the statement (ii) ‘Ismael Lowenstein is the son of Mario and Amanda Belinzoni’ would not be necessary a posteriori. It would be rather seen by the Nazis as contingent a posteriori, as far as they still have achieved only an inductive certainty of its truth, except if they decide to use it stipulatively as a necessary a priori statement.

2. Worst than the necessary a posteriori is a later invention of Kripke called contingent a priori. It is the case involving the platinum rode in Paris that once defined the meter as the unity of length. According to him, analysis of meaning is something different from a definition; the first is necessary, but the second not.  The definition of ‘one meter’ as ‘the lenght of S at to’ was a priori but contingent. Moreover, ‘one meter’ is a rigid designator while ‘the length of S at to,’ being a definite description, is an accidental designator, allowing making the lengh possibly longer or shorter than one metter, for instance, by earlier heating or cooling. Therefore, the statement ‘Paris platinum rode is one meter long’, though established a priori, is contingent, for it could be different. (Kripke 1980: 56).
   A difficult it that Kripke gives no satisfactory reason for this conclusion. The definition of one meter as ‘the lenght of S at to’ is a stipulative definition establishing a new meaning. Beside this, why cannot ‘one meter’ be an abbreviation of ‘the length of S in ∆t[8], whoever this length is,’ as it seems? Assuming this, our intuitive reasoning would be to think that if the lenght changes the meter itself isn’t different, since the standard meter is defined as whatever length S has when used as a pattern. Being so is recomendable to have the most uncheangeable possible standard metter. For suppose that the standard metter were something elastic, always changing. It would still remain the same standard meter, for sure, but it would be very unpratical. Using this standard according to the given definition we could be forced to say of a man who was 1:76 m high two hours ago that he is 2:24 m high right now, or that two object with very different sizes would have the same size only because they were measured in different times… Anyway, if you consider that the statement ‘One meter is the length of S in ∆t’ presents the definition of a standard meter – and it really does – this definition is necessary, since it is conventional and cannot be falsified in any possible world in which it holds; moreover, this definition is a priori, for we don’t need to have any experience to know its truth (it exemplifies the law of identity). Consequently, the definition:

Paris platinum rode is one meter long in ∆t as a standard to be met in any circumstance.

is a necessary a priori truth, not a contingent a priori one.
   Now, if you decide to treat it differently, comparing different possible standard meters in different times or different counterfactual situations, then you are reading the statement ‘Paris platinum rode is one meter long’ as something like ‘The standard meter in w1 has the same length as the standard meter in w2 (or in a counterfactual situation)’. In this case it means more precisely:

Paris platinum rode is one meter long during ∆t only if compared with others standard meters that could be used as standards in different times or in any counterfactual circumstances.

This, of course, is imposible. Because Kripke sees that the standard meter cannot perform this funcion he comes to the conclusion that it must be contingent. But this function was never required. Consequently, the standard metter isn’t contingent: it is, as we saw, a necessary a priori stipulation.

3. Another attempt to exemplify the contingent a priori could come from Gareth Evans’ example with the name ‘Julius’, which is artificially stipulated as ‘the inventor of the zip’ (Evans 1982: 31). According to some the statement ‘Julius was the inventor of the zip’ is contingent a priori. It is a priori because we don’t need the experience to know this. But it is also contingent since it is possible that he droped on his head when little, growing up too stupid to invent the zip (Papineau 2012: 61).
   Here again we have a twofold understanding. Since it is possible that no one invented the zip or that several persons invented it… the statement can be false. Under this reading ‘Julius invented the zip’ is a contingent a posteriori statement. But we can also read this statement as a necessary a priori one, under the assumption that someone really invented the zip. In this case it is a priori because under this assumption it is known as true independently of the experience. But it is also necessary, since it is a linguistic stipulation replacing the real name of the person we are assuming to have invented the zip.

4. A related funy example is the following utterance: ‘I am here now.’ According to David Kaplan, this is also a kind of contingent a priori truth. It is a priori because since each one of its terms refers directly respectively to the agent, the place and the time of a given context of utterance, the possibility of its falsity is excluded. But since we can imagine counterfactual circumstances in which I would not be here, its utterance is only contingently true (Kaplan 1989: 509).
   This example is also delusive. For ‘I am here now’ can be false in the actual world too. I remember a case related by Dr. Oliver Sacks of a pacient who had a seriously deranged perception of the continuity of time. Because of this, her daily life was formed by time lapses: she could think ‘I am here now’ as if she were still in the sleeping room, when in fact she had already moved to the kitchen. So, in this case ‘I am here now’ empirically false. So understood it is a contingent statement, which is also a posteriori, since dependent on the context of the experience.

4. A not very dissimilar line of reasoning concerns my objections against Hilary Putnam’s view that the meaning of the word ‘water’ must be external to our heads. This is perhaps the most influential argument for semantic externalism. According to Putnam’s thought-experiment, in 1750 Oscar-1 in the Earth and Oscar-2 in the Twin-Earth – both nearly identical planets with the same history – seeing that it rains, could have only the same idea of a watery liquid (an under normal temperatures transparent, inodorous, tasteless… liquid) within their heads. However, without their knowledge, they were refering to very diferent composits, the first H2O and the second XYZ, since the water in the Twin-Earth has a very different chemical composition, summarized by Putnam as XYZ, though with the same apparence and effects. For Putnam this proves that the meaning of water – which for him concerns essentially amounts of atoms with the same microstructure H2O – wasn’t in the heads of the Oscars, since in their heads they had the same thing, namely, the idea of a watery liquid. Consequently, the meaning isn’t in the head. As he in a central passage wrote:

Oscar-1 and Oscar-2 understood the term ‘water’ differently in 1750, although they had the same psychological state, and though, given the state of development of Science in their epoch, the scientific community would need to take circa 50 years to Discovery that they understood the term ‘water’ differently. Hence, the extension of the term ‘water’ (and, in fact, its meaning in the pre-analitic intuitive use of the term isn’t function of the psychological state of the speaker. (My italics)[9]

This schocking conclusion was later radicalized by John McDowell, who concluded that even the mind is external to the heads because it is the locus of our manipulation of meanings (1992: 36).
   My neodescriptivist answer is that Putnan’s result comes from the overseen of the fact that the word ‘water’ has in fact two descriptive nuclei of meaning, a popular and a scientific one.[10]  First there is an old popular nucleous of meaning of the word ‘water’, which is phenomenal or dispositional and can be summarized in the expression ‘watery liquid’ (the under normal temperatures transparent, inodourus liquid, that quenches the thirst, extinguish the fire, has high superficial tension, falls als rain, fulfills rivers, lakes and oceans, when colded turns to ice, when warmed to steem, etc.). This was the only meaning in the market until the beginning of the XIX century. Then a new meaning was increasingly additioned: the scientific nucleous of meaning, which can be summarized as ‘quantities of H2O’ (which results from 2H2 + O2 = 2H2O, can be subjected to electrolysis, forms intermolecular hydrogen bounds responsible for its high superficial tension, etc.). Both nuclei of meaning are obviously descriptive (since the domain of the descriptive is much wider then the merely phenomenal domain) and are presented today in any good dictionary.[11] Furthermore, it is easy to see that in consonance with the variability of the context, one of these meanings comes often to the fore.
   This analysis already allows a convincing internalist explanation to the Twin-Earth fantasy. In 1750 the two Oscars had only the meaning ‘watery liquid’ in their heads, so that the extension of the word water were the same for them. But when Putnam considers what is going on, he is unconsciously projecting the diferent scientific meanings of the word water in the actions of the two Oscars, treating them as indexical devices for the projection of these diferent meanings whose true locus is in fact I our own heads, since Oscar-1 is pointing to H2O, while Oscar-2 is pointing to XYZ. Consequently, the different scientific meanings of the word ‘water’ are not in the world and out of our heads, as Putnam believes, but in Putnam’s head when he thinks his thought-experiment and in our heads when we read him, since we all today know the scientific core of meaning. And since Putnam and his readers have different scientific meanings in their heads when unconsciously projecting them to Oscar-1 and Oscar-2 by using them as indexical devices, these different meanings remain, as it should, internal properties of minds.
   This idea is reinforced within the neodescriptivist view that I suggest by the consideration that the meaning of ‘water’ varies with the context of interest in which the word is used. In a scientific context of interest (e.g., in a laboratory of chemistry) ‘Water is H2O’ means (a) ‘Hidroxid of oxygen = H2O’: an analytic statement. In this context even if water were not a watery liquid, but something like coal, it would still be called water, as far as it preserves the right microstructure.
   Now, in a popular context of interest (e.g., of fishermen wishing to use water for drinking and washing) ‘Water is H2O’ is an a posteriori contingent statement that can be made false, since the privileged sense is here ‘Water = watery liquid’, so that the substitutional sentence would be (b) ‘Watery liquid = liquid composed of H2O’, and this identity not only isn’t known without experience but the composition of the watery liquid as H2O isn’t necessary.
   Conclusion: Putnam’s and Kripke’s classification of the statement ‘Water is H2O’ as a necessary a posteriori statement is only a confusion between the necessity of the statement (a) and the a posteriori nature of the similar statement (b), resulting from lack of attention to the pragmatic of natural language. We already spoke about these kinds of confusion as we examined Wittgenstein’s account of the transgressions of the internal limits of language.
   The point can be easily generalized. Consider the statement (i) ‘Hydrogen is a gaz containing atoms with one proton and one electron.’ One could say: though necessary, it was discovered a posteriori. But in fact it has at least two contextualized senses: First, if you think of the transparent inflammable gas discovered by Cavendish in 1766 and called by him ‘unflammable air’, which was later analysed as constituted by atoms with one electron and one proton. In this case statement (i) is read as contingent a posteriori; this gas could have a different atomic structure and one could spell the same statement as (i-a) ‘Inflammable air is constituted by atoms containing one proton and one electron.’ On the other hand, after we conventionally established the meaning of hydrogen as a gaz containing atoms with one electron and one proton (as we do definitionally in science today), (i) will be read as a necessary a priori statement, because it could be unpacked as (i-b) ‘Hydrogen (Df) = the gaz constituted by atoms containing one proton and one electron’, assuming the truth of modern chemistry.

6. There are two others examples of Putnam aiming to show that the meaning is not only in the external physical world, but also in the society.[12] In the first one, Putnam assumes that aluminium and molybdenium are only distinguishable by metalworkers and that the Twin-Earth is full of molybdenium used to build pots and pans. In addition, he imagines that the inhabitants of the Twin-Earth call molybdenum ‘aluminium’. In this case, he writes, the word ‘aluminum’ said by Oscar-1 will have an extension different than the word ‘aluminum’ said by Oscar-2, so that they mean different things with the word. But as they are not Steelworkers, they have the same psychological states. Hence, the real meaning of these words is external to what happens in their heads, depending on the society.
  Our answer is as follows. If we consider the words ‘aluminium’ and ‘molybdenium’ in the way they were used by Oscar-1 and Oscar-2, the Oscars are unable to really decide if what they have is aluminium or molybdenium, since they are not experts and what they have in their minds is indeed the same, as much as the extension that they can give to their concept of aluminium. For the metalworkers of Earth and Twin-Earth, on the other hand, the aluminium and molybdenium have very different constitutive properties, what means that they would have something different in their heads, though they use these words with exchanged meanings. The Oscar’s may confuse both things, but only because they do not know really what these things are: they are using the words in a subsidiary sense. Finally, we can consider the aluminium and the molybdenium observed by Oscar-1 and Oscar-2 and take both persons as referential devices, so that we would say that Oscar-2 is pointing at what his linguistic community calls aluminium, but which is what we in our linguistic community call molybdenium. That we should use our words in accordance with the conventions of our linguistic community does not make the meaning external, only dependent of the agreements under the members of this community.
   In the second example Putnam consider the difference between olms and beechs. Most of us do not know how to distinguish olms from beechs in a forest. However, we are able to assume that these words have different extensions. So, what we mean with these words are different, though we do not have different concepts and the difference isn’t in our heads... Consequently, their meanings are external: the physical world and the society with its specialists are are those who have the hability to fix the referential meaning of these words.
   The important point to be noted is that we in fact do have an insufficient knowledge of the meaning of the words ‘elm’ and ‘beechs’. But we already know something very generic about them: we surelly know that they are trees and almost certainly distinct kinds of trees. With help of these convergent descriptions (see appendix of chapter 1, sec 4) we are able to insert these words into the discurse, often waiting for the distinguishing information given by the specialists. The last are the persons who have the sufficient knowledge of the meaning of these words, enabling them to identify the different kinds. But the meaning, sufficient or not, is always in the heads of the speakers.[13]
   Putnam appeals to a division of labour of language in order to explain the different aspects of meaning that may be considered by different speakers. This is an important idea. But this isn’t an idea that confirms an externalist conception of meaning. It is rather neutral, for the idea of a division of labour of the language was already suggested by internalist philosophers from John Locke to C. S. Peirce (Smith 2005: 70-73). In effect, this idea is perfectly compatible with the difference in the fact that, even if being socially shared, the meaning remains in the heads of the speakers, specialists or not, in different dimensions and degrees. In none of the cases above the meaning needs to be outside the heads.

7. Now I wish to reinforce my anti-externalist arguments discussing Tyler Burge’s social externalism of thought concerning the concept of arthritis, which is complementar to Putnam’s argument. What Burge intended was, apart from Putnam, to show that not only the meaning is outside the head, but the beliefs’ extension, i.e., the proper content of thought (Burge 1979).
   I will first summarize the argument of Burge and then show that it is easy to find a much more plausible weak internalist explanation for what happens, simply by developing an objection already made by John Searle (2004: 284-6). In order to make it clearer, instead of following Burge’s counterfactual mental experiment, I will first suppose that a person with the name Oscar feels pain in the thigh and see a doctor saying:

(i) I think I have arthritis in the thigh.

Since arthritis is characterized as a painful inflammation of the joints, the doctor sees that his belief is false, for one cannot have arthritis in the thigh. Imagine now Oscar-2 in the Twin-Earth visits a doctor for the same reason. But although in the Twin-Earth all things occur nearly as in the Earth, the people use the word ‘arthritis’ in a much broader sense, referring to any kind of inflammation. Suppose that in this second linguistic community Oscar-2 says to the doctor (i) ‘I think I have arthritis in the thigh’, having in mind exactly the same as in his first utterance. In this place, as one would expect, the doctor will confirm the suspicion, agreeing that this is an unquestionably true belief.
   Based on this example, Burge’s reasoning goes as follows. Without doubt, the psychological States of Oscar-1 and Oscar-2, when they said to have arthritis in the thigh are exactly the same, as well as their behaviour. But the contents of thought expressed in the two utterances must be different, since the thought expressed by the first utterance is false, while the thought expressed by the second is true, and the same thought cannot be false and true. We can even mark the second meaning of the word ‘arthritis’ on the utterance of Oscar-2 with a new word: ‘tharthritis’. Burge’s conclusion is that the contents of thoughts cannot be merely psychological.[14] These contents must belong also to the outside world, to the social communities involving the speakers.
   Against this conclusion it isn’t difficult to find a commonsensical internalist-descriptivist explanation for what happens. For this healthy internalism (which admits that our mental subjectivity unavoidably depends on external inputs), in the Twin-Earth the concept-word ‘arthritis’ is the expression of an ascription rule constitutive of its meaning, which is more general, designating any kind of inflammation. According to this rule, ‘an inflammation that occurs in the thigh’ serves as a criterial condition and belongs to the sense of the word in the linguistic community of the twin-Earth, though not in the linguistic community of our Earth. Thus, although the thought expressed in the sentence ‘I think I have arthritis in the thigh’ said by the Oscars in the two linguistic communities are exactly the same, there is a fundamental difference that was rightly recalled by John Searle in the following words:

Our use of language is presumed to conform to the other members of our community, otherwise we could not intend to communicate with them by using a common language. (Searle 2004, 184-5)

That is, when Oscar-1 says to the doctor of the Earth ‘I believe I have arthritis in the thigh,’ he must be dispositionally assuming that his generalised ascription rule for the predicate ‘arthritis’ belongs to the language that the other competent speakers of the language conventionally apply. The whole of what Oscar-1 has in mind (not only actually but also dispositionally) in his utterance in the Earth’s linguistic community is:

(a)  I have arthritis in the thigh… [and I am assuming that the generalised criterial condition for the ascription of the predicate ‘arthritis’ is accepted as correct by the linguistic community speakers to which belongs my present interlocutor D1].

This is false because the second sentence of the conjunction is false. Let’s now see what is (actually and dispositionally) meant when Oscar says he has arthritis in the thigh to the second doctor:

(b) I have arthritis in the thigh… [and I am assuming that the generalised criterial condition for the ascription of the predicate ‘arthritis’ is accepted as correct by the community of speakers to which belongs my present interlocutor D2].

Now the statement (b) is true. Although the statement ‘I have arthritis in the tight’ says the same, it has a hidden indexical meaning that differs from (a) to (b). And this hidden indexical content is in the minds of the Oscars. So, it may be true that if we confine ourselves to the content expressed in the thoughts of the Oscars in making the same utterance in both places we see them as identical. But the whole of what they have mind (that is, in their heads) with each utterance are different because in the first Oscar-1 knows that he is speaking with doctor D1 belonging to the linguistic community of the Earth, while in the second he is aware that he is speaking with doctor D2 at a linguistic community of the Twin-Earth.
   This assumption that the verifiability rules constituting the content of thought should be in accordance with the conventions of the comunity of language in which it is expressed in order to achieve truth is infringed by Oscar when he speaks with the doctor the community belonging to the earth, but it isn’t infringed when Oscar speaks with the doctor of the community belonging to the Twin-Earth.
   Nonetheless, Burge has called us attention to one important thing: that the truth or falsehood of utterances depends on the linguistic conventions adopted by the community involving the speaker. This is an already relevant point, though it does not reach the claim that anything of a thought-content or belief is outside the internal psychological realm, in some way dispersed in the external social-physical environment.
   Finally, the given explanation allows us to make a healthy internalist paraphrase of the well-known distinction between narrow content and wide content. For the unmasked externalist point of view, the narrow content is one that is in the mind of the speaker, while the wide content is external: it is out there in the world or in the society. The healthy internalist analysis of Burge’s example allows us to propose that the narrow content of thought is the semantic-cognitive verifiability rule that constitutes it (expressed by the statement ‘I think that I have arthritis in the thigh’), while the wide content of thought is what is assumed in the speaker’s mind as a provision whose expected existence will be arguably accepted.

8. Finally, one word about John Perry’s argument for the essential indexical (1979). I will be extremely short, since I am repeating an argument presented in details in another place (Costa 2014c). His view is that senses of indexicals are inevitably tied with the external circunstances of utterance, what can be proved by the fact that one cannot translate them into eternal sentences without loss. Consequently, externalism is correct.
   In Perry’s main example he is in a supermarket and discovers that there is a trail of sucar on the floor. He begins to search for the author of the trail only to discover that the person who is spilling sucar out of the car is he himself, what leads him to say: (i) ‘I am making a mess’, what immediately changes his behavior. Suppose, says Perry, that he translate this statement in the non-indexical statement (ii) ‘Perry is making a mess’. It is not the same, since he could, for instance, be suffering from Alzheimer, having forgoten that his name is Perry…
   However, I think that there is indeed a way to preserve the sense of the indexical detaching it from the context. It is a technique that I call transplantation: if you need to change the place of a plant you usually don’t take the plant alone, but the plant with the earth in which it is inserted, often together with the whole covering. Applying a similar technique, here is how Perry’s example appears after transplantation:

(iii) At 10:20 a.m. on March 26, 1968 in the confectionary supplies of the Fleuty Supermarket in the city of Berkeley, CA, after noticing a sugar trail stretching away from his shopping cart, Perry says to himself that he is making a mess.

Here what counts is the truth of the eternal sentence into which the indexical sentence is included. Although containing an indexical (he, himself), the statement (iii) is not refering to the real context, but referring indirectly to the fregean thought expressed within the subordinate sentence after the that-clause. Thus, protected by its surrounding description (the covering of the eternal sentence) the sense of ‘I am making a mess’ is here integrally transplanted without loss into the non-indexical context that would be called by Frege indirect reference.[15] What this argument shows is that essential indexicals are not essential, once the external components can be internalized.




[1]  As he says: ‘What I do deny is that a particular is nothing but a ‘bundle of qualities’, whatever that may mean’, meaning by ‘qualities’ abstract entities (1980: 52).
[2] It seems that the real reason why we distinguish the regularities that are natural laws from those that are merely coincidental is that the first are well-entrenched, that is, are strongly inferentially bounded with our scientific system of beliefs. This is what gives them the impression of logical necessity. It is true that we have in the present discussion several alternative approaches to this classic Humean regularity view. But first, the regularity view seems to be the most plausible approach, regarding the assumption of fallibility; second, the fact that something is presently very much on the stage is within the intrinsically changeable landscape of philosophy no value judgment.
[3] Later he also wrote: ‘It might be imagined that some propositions, of the form of empirical propositions, were hardened and functioned as channels for such empirical propositions that were not hardened but fluid; and that this relation altered with time, in that fluid propositions hardened, and hard ones became fluid.’ (Wittgenstein 1984a sec. 96)
[4] For a complementary approach, see chap 4, sec. 22.
[5] According to Kant there is priori knowledge that isn’t pure, taking long exercise to be separated from the knowledge adquired by means of sensory experience (Kant 1787: Introduction, I).
[6] Kripke speaks of Elisabeth II, the Queen of England, an example in which the ovulo origin acquires maximal importance, contaminating the characterizing description of its identifying rule.
[7] There are today several competing theories of parenthood (genetic, labour-based, intentional, causal and pluralistic accounts) and there is no consensus on the right cluster of criteria (see Brake & Millum 2016, sec. 4).
[8] The symbol ‘∆t’ is more correct because, of course, the road serves a standard not only in to but during all the time in which it is conventionally designed to this function.
[9] Hilary Putnam: “The Meaning of ‘Meaning’” (1995: 224).
[10] I am strongly summarizing here. For the full argument, which is preceded by a more careful neodescriptivist analysis of the meanings of the word ‘water’, see Costa 2014b.
[11] For instance, the main definition in the Merrian Webster dictionary contains elements of both, popular and scientific nuclei of meaning: ‘water = the liquid that descends from the clouds as rain, form streams, lakes, and seas, and is a major constituent of all living matter and that when pure is an odourless, tasteless, very slightlty compressible liquid oxide of hydrogen H2O which appears bluish in thic layers, freezes at 0°C freezes and boils at 100°C, has a maximum density at 4°C and a high specific heat, is feebly ionized to hydrogen and hydroxy ions, and is a poor cinductor of electricity and a good solvent.’ (See Stroll 1996)
[12] To be fair, Putnam expresses himself more carefully in a later writting by saying that the meaning is determined by the external world. But either we understand this in the sense that it is the external world that ultimately produces referential meanings in our minds, what is an obvious truism that as a weak internalist I have no desire to deny, or what he means with the word ‘determination’ remains a too subtle metaphor to find any rescue (See Putnam, 1988, ch. 2).
[13] For interesting answers to some others externalist arguments see Searle 2004.
[14] As he wrote: ‘The upshot of these reflections is that the patient’s mental contents differ while his entire physical and non-intentional mental histories, considered in isolation from their social context, remain the same.’ (Burge 1976: 106, my italics) 
[15] See appendix of chapter 4, sec. 5 (iv).