I want now to introduce a kind of fission example that I claim is invulnerable to recent neoconservative attempts to show that identity really is what matters in survival. I shall use the example to support two ideas: first, that for many people identity is not what matters primarily; and, second, that for those same people there is no reason to think that identity should be what matters primarily. In arguing for these ideas I shall assume that the question of what matters in survival is best approached from a thoroughly naturalistic perspective, hence, that personal identity is not best explained by appeal to spiritual substances, to immaterial souls, to any sort of supposedly essentially indivisible entity, and so on. All of the neoconservatives whose views I am going to consider would grant such assumptions.

THE EXAMPLE: FISSION REJUVENATION

John is twenty years old. Physically and psychologically he is in very good shape. He is handsome, healthy, and vital. He knows that even without undergoing fission rejuvenation his prospects are good for a long and happy life. He also knows that he will never be in better physical condition, never better positioned, to undergo the procedure. He worries that already he may have waited too long.

In the morning John will go to the hospital, where he will be put under a general anesthetic and then have his brain divided into functionally equivalent halves, each capable of sustaining his full psychology.

Most adults during most of their waking hours experience what they take to be themselves as perceivers. By “most adults” I mean most in modern industrialized cultures; people in so-called primitive cultures may be different. By “most adults experience what they take to be themselves as perceivers” I mean, roughly, that when most adults experience either their own internal states or objects in the world, they simultaneously experience what they (mistakenly) take to be themselves as fixed, continuous points of observation on those internal states or external objects. By “fixed” I do not mean fixed forever or fixed absolutely, but rather relatively stable as compared with the dynamism of most of the rest of experience.

I call this illusory experience of self the perceiver-self phenomenon. It is, I think, a profound form of alienation and, hence, of human suffering. And I think it figures importantly in the formation of core human values and in fear of death. However, in this chapter I want only to defend the much more modest claim that the influence of this phenomenon needs to be taken into account to understand surrogate-self-identification, in particular, why people tend to surrogately self-identify with certain real and hypothetical continuers and not with others.

First, I want to answer those philosophers - nurtured on Book I of Hume's Treatise - who are skeptical that they ever, let alone almost always, experience what they take to be themselves as perceivers.

we are now in a position to undertake a closer examination of the details of the actual projects for achieving objectivity presented in Der logische Aufbau der Welt. An outline of Carnap's levels of constitution is, therefore, in order. In this way, we will be able to see what Carnap is doing in his two projects. Again, many questions about constitution and the order of the definitions will not be addressed in order to focus our attention solely on the question of the way the constitutional system explicates the objectivity of scientific claims.

THE LOWEST LEVELS OF THE CONSTITUTIONAL SYSTEM

The constitutional system meant to mirror the epistemic primacy relation begins, as we have noted, from a single relation, the “recollection of similarity” relation (Rs), over total cross-sections of experience at a time. Carnap's first order of business in the constitutional system is to constitute the rich texture of individual psychological life, the auto psychological domain, from this slender basis (cf., esp. §§108–20). Our primary concern is with the role of the auto psychological domain in the construction of objectivity, so I shall only sketch the definitions here. Of primary importance for our purposes is the final accounting of the auto psychological domain and the transition to the world of physics.

Before discussing the definitions, there is a noteworthy aspect of Carnap's procedure that warrants a brief mention. In accordance with the methodological strictures of “purely structural definite description” (PSDD), the definitions depend only on the structure of the recollection of similarity relation, but this structure is itself only empirically known.

all the creative Kantian reconstruction in Chapter Four was not simply make-believe, although it may well have been a bit of “leading” history. It was, indeed, designed to lead naturally into a discussion of the foremost neo-Kantian thinking on the exact sciences in the first quarter of the twentieth century. I have in mind neo-Kantian philosophy as articulated by authors such as Ernst Cassirer (1910, 1921), Bruno Bauch (1911, 1914), and Paul Natorp (1910a, 1910b). I shall consider only the works of these three philosophers in this chapter, because they are the neo-Kantians who most influenced Carnap's thinking. Bauch was Carnap's dissertation director and the philosopher from whom Carnap learned what he knew about Kant. Cassirer's Substanzbegriff und Funktionbegriff (Substance and function) (1910) was clearly the most systematic discussion of the general neo-Kantian line on science and mathematics; as we have already seen in Chapter Two, Carnap's references to it in Der logische Aufbau der Welt show a deep appreciation of some of its central points. Moreover, Cassirer's (1921) monograph on the theory of relativity, Zur einstein'schen Relativitdtstheorie (On Einstein's theory of relativity) was the most methodologically sophisticated and technically informed neo-Kantian discussion of the issues raised by relativity. As for Natorp, Carnap, in a letter to the conventionalist physicist Hugo Dingier in 1920, indicated that Natorp was the neo-Kantian whose views on mathematics and physical methodology had most occupied his thinking during the writing of his dis-sertation.

Each of us identifies with himself in the past and in the future in a way in which normally we do not identify with anyone else. We identify with ourselves in the past primarily by remembering having had experiences and having performed actions. We identify with ourselves in the future primarily by anticipating having experiences and performing actions. Ordinarily we remember or anticipate having only our own experiences and performing only our own actions. That's because ordinarily our options include only those we have in real life.

As we have seen, there are hypothetical situations in which many of us would anticipate having the experiences and performing the actions of continuers of ourselves who, apparently, we do not think are ourselves and who, on many of the criteria of identity to which philosophers subscribe, are not ourselves; and we would anticipate having these experiences and performing these actions in pretty much the same ways we currently anticipate having our own experiences and performing our own actions. In other words, there are hypothetical situations in which, apparently, many of us have identificatory surrogates. As we have also seen, for those who are three-dimensionalists about persons the case that many of us have identificatory surrogates can be made by appeal to fission examples; but the case itself, whether it is being made for three- or for four-dimensionalists, does not depend on fission examples. It can be made without them.

Occasionally, but not often, philosophers discover something genuinely new - a new problem or a subtle change in an old problem that brings a new set of issues into focus. When this happens circumstances are ripe for transformations not just of what we believe but also of what we think is worth considering and how we think we ought to proceed.

Beginning in the late 1960s something genuinely new happened in the centuries-old philosophical debate over personal identity; more precisely, something new would have happened, had it not happened once before, in the eighteenth century (this earlier discussion then was forgotten). What was new, on both occasions, is that tacit and extremely natural assumptions about the importance of identity in a person's so-called self-interested concern to survive were called into question. As a consequence, the traditional philosophical focus on metaphysics gave rise to new normative and empirical inquiries about what matters in survival. In these new inquiries fundamental and potentially unsettling questions were raised, for the first time (and as if for the first time), about the significance of the distinction between self and other.

The revolutionary and controversial thesis that identity is not what matters primarily in survival has been a principal focus of the more recent debate. The version of this idea that has gotten by far the most attention is the normative thesis that identity is not what should matter primarily in survival. This normative thesis has been endorsed by several influential philosophers.

We never vanish without a trace. Even in death, the stuff into which we decompose continues. Most of it is recomposed into other things, often things that are alive. We are food for worms. For those of us who want to continue, these facts are small comfort. Why exactly? For many of us, at least at the level of theoretical belief, it is not, I want to claim, because transformation is not good enough - because we want to preserve our identities; rather, it is because we do not identify fully with the things into which we expect to transform. If we were to identify fully with the people (or whatever) into which we expect to transform, many of us, as we shall see, would be happy to forfeit our identities provided we could secure certain other benefits.

Identity counts for something, so the value of these other benefits would have to outweigh the value of identity. But for many of us identity is not so valuable that it is difficult to think of benefits that might outweigh it. The trades many of us would be willing to make, and might rationally make, show, I think, that for many of us neither robust physical continuity nor robust psychological continuity either does or ought to matter primarily in survival. Whether the same nonfission examples can be used to show that not even minimal physical or psychological continuity matters primarily is a more difficult question.

The distinction between analog and digital representation of numbers is well understood in practice. Yet its analysis has proved troublesome. I shall first consider the account given by Nelson Goodman and offer examples to show that some cases of analog representation are mis-classified, on Goodman's account, as digital. Then I shall offer alternative analyses of analog and digital representation.

DIFFERENTIATED ANALOG REPRESENTATION

According to Goodman in Languages of Art, the distinction between digital and analog representation of numbers is as follows. Digital representation is differentiated. Given a number-representing “mark” – an inscription, vocal utterance, pointer position, electrical pulse, or whatever – it is theoretically possible, despite our inability to make infinitely precise measurements, to determine exactly which other marks are copies of the given mark and to determine exactly which number (or numbers) the given mark and its copies represent. Analog representation, on the other hand, fails to be differentiated because it is dense. For any two marks that are not copies, no matter how nearly indistinguishable they are, there could be a mark intermediate between them which is a copy of neither; and for any two marks that are not copies and represent different numbers, no matter how close the numbers are, there is an intermediate number which would be represented by a mark that is a copy of neither.

It is true and important that digital representation is differentiated, and that it differs thereby from the many cases of analog representation that are undifferentiated and dense: those cases in which all real numbers in some range are represented by values of some continuously variable physical magnitude such as voltage.

COUNTERFACTUALS AND FACTUAL BACKGROUND

Consider the counterfactual conditional ‘If I were to look in my pocket for a penny, I would find one’. Is it true? That depends on the factual background against which it is evaluated. Perhaps I have a penny in my pocket. Its presence is then part of the factual background. So among the possible worlds where I look for a penny, those where there is no penny may be ignored as gratuitously unlike the actual world. (So may those where there is only a hidden penny; in fact my pocket is uncluttered and affords no hiding place. So may those where I'm unable to find a penny that's there and unhidden.) Factual background carries over into the hypothetical situation, so long as there is nothing to keep it out. So in this case the counterfactual is true. But perhaps I have no penny. In that case, the absence of a penny is part of the factual background that carries over into the hypothetical situation, so the counterfactual is false.

Any formal analysis giving truth conditions for counterfactuals must somehow take account of the impact of factual background. Two very natural devices to serve that purpose are orderings of worlds and sets of premises. Ordering semantics for counterfactuals is presented, in various versions, in Stalnaker [8], Lewis [5], and Pollock [7]. (In this paper, I shall not discuss Pollock's other writings on counterfactuals.) Premise semantics is presented in Kratzer [3] and [4].

INTRODUCTION

As explained in the previous chapter, the moderate empiricist position on a priori knowledge holds that while such knowledge genuinely exists and has occasional importance in its own distinctive way, it is nonetheless merely analytic in character – that is, very roughly, merely a product of human concepts, meanings, definitions, or linguistic conventions. Such knowledge thus says nothing substantive about the world, and its justification can be accounted for without appealing to anything as problematic as the rationalist idea of rational insight into the character of an sich reality. Indeed, as we shall see later in this chapter, it is this alleged capacity to provide an unproblematic explanation of a priori justification that constitutes the main argument for moderate empiricism, even in the face of recalcitrant rationalist counterexamples.

For much of this century, this general sort of position had the status of virtually unquestioned orthodoxy for most philosophers in the Anglo-American tradition; and despite the recent prominence of the radical empiricist views that will be discussed in the next chapter, it seems likely that moderate empiricism continues to be the most widely held view of the nature and status of a priori justification. What is profoundly misleading about the foregoing picture, however, is the suggestion that there is anything like one reasonably specific position that can be identified as moderate empiricism.

INTRODUCTION

In this appendix, I will try to say something about the implications of non-Euclidean geometry and especially its role in the theory of General Relativity for a rationalist view of a priori knowledge. There can be little doubt that from a historical standpoint, the development of non-Euclidean geometries was a major factor in producing the widespread conviction that a rationalist position is untenable. Euclidean geometry was after all the most striking example of seemingly substantive a priori knowledge of independent reality, invoked by Kant as one of the crucial examples of the synthetic a priori. But, according to the simplest version of the standard story, within a few years after Kant, the development of non-Euclidean geometry by Lobashevsky and others showed that Euclidean geometry was not necessarily true of physical space, making it an empirical issue which geometry correctly describes the physical world. And eventually, or so the story goes, this empirical question was resolved by General Relativity in favor of a version of Riemannian or elliptical geometry and against Euclid. The suggested further argument, often left fairly implicit, is that if the rationalist view fails in this paradigmatic case, there can be no good reason for thinking that it will in the end be any more acceptable elsewhere.

Mereology is the theory of the relation of part to whole, and kindred notions. Megethology is the result of adding plural quantification, as advocated by George Boolos in [1] and [2], to the language of mereology. It is so-called because it turns out to have enough expressive power to let us express interesting hypotheses about the size of Reality. It also has the power, as John P. Burgess and A. P. Hazen have shown in [3], to simulate quantification over relations.

It is generally accepted that mathematics reduces to set theory. In my book Parts of Classes, [6], I argued that set theory in turn reduces, with the aid of mereology, to the theory of singleton functions. I also argued (somewhat reluctantly) for a ‘structuralist’ approach to the theory of singleton functions. We need not think we have somehow achieved a primitive grasp of some one special singleton function. Rather, we can take the theory of singleton functions, and hence set theory, and hence mathematics, to consist of generalisations about all singleton functions. We need only assume, to avoid vacuity, that there exists at least one singleton function.

But we need not assume even that. For it now turns out that if the size of Reality is right, there must exist a singleton function. All we need as a foundation for mathematics, apart from the framework of megethology, are some hypotheses about the size of Reality.

(Megethology can have no complete axiom system; and it would serve little purpose to fix upon some one official choice of an incomplete fragment.