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Absolute identity/unity.

ANY SEARCH FOR THE FUNDAMENTAL NOTIONS by which we might conceive of the world will have to consider the notion of identity as a very serious candidate. Identity is presupposed in mathematical equations, in the sameness of particles or fields in quantum field theory, and in logical laws like noncontradiction and the excluded middle. (1) In spite of its fundamentality--or perhaps even because of it--the notion of identity is iridescent. Logical and ontological aspects are inextricably interwoven. Some investigations of identity try from the start to separate these aspects and to concentrate on the logical features of identity. However, ontological questions or tacit assumptions normally emerge very soon. So it seems reasonable to try another look at identity, from an ontological point of view. I will also use the term "unity" to signify this alternative perspective.

In this paper the ontologically strongest possible meaning of identity/unity will be scrutinized. But in order to acquire a full understanding of this strong meaning of identity and to relate it to weaker alternatives, it seems useful to approach this by a sort of semantic and ontological ascent, by recapitulating some of the weaker and more familiar meanings first.

(1) In its weakest sense, "identity" refers to sameness of some or all relevant qualities of different objects (identity of qualities). (2) (2) In a stronger sense, it can be understood as sameness of objects or substances (numerical identity), which certainly does not exclude the existence of more than one such self-identical object or substance. (3) Although it seems to be possible to understand numerical identity without connecting the numerically identical objects to predicates, such a connection is frequently discussed in two further proposals: (3) some commentators speak of "relative identity," whereby--according to one interpretation--numerical identity and identity of qualities cannot be combined in such a way that one would follow from the other; (4) (4) there is an even stronger, epistemological and ontological meaning which affirms just this inference from the identity of qualities to numerical identity and/or vice versa--the identity of indiscernibles and the indiscernibility of identicals (both principles known as Leibniz's Law (5)). Sometimes numerical identity within Leibniz's Law is called "absolute identity," especially to differentiate it from "relative identity." But this terminological coinage is questionable because "absolute" means "without relation," and Leibniz's Law rests on the relation between numerical and qualitative identity. Therefore in what follows the notion of "absolute identity" shall be reserved for an even ontologically stronger understanding; (5) finally there is the strong ontological notion, which can be found in the monism of Parmenides and Spinoza, of an all-identity, an identity of everything with everything in the form of one and only entity or substance. (6)

However, the last meaning of all-identity is not the strongest ontologically possible understanding of identity and therefore not the most crucial one for our ontological understanding of the world because all-identity can be differentiated internally, as Spinoza assumed in respect to attributes and modi. (7) Parmenides allowed internal relations too, (8) and so did Bradley. (9) The ontologically strongest possible form of identity would be one of an all-identity (as in 5) without any internal differentiation. In what follows, I shall name this strongest ontologically possible notion of identity (6) "absolute identity." One could certainly also consider using the terms "unity" or "totality." But these terms seem always to imply the unity or totality of "something," which demands at least some sort of internal differentiation of entities. Even if one would speak of the "unity of everything", "everything" would refer to a multiplicity ("every") of "things." Instead, "identity" understood as numerical identity seems to allow but not to require a multiplicity of entities or a connection with properties. So by alluding to this specific aspect of numerical identity, "absolute identity" might be the best solution among all unsatisfactory alternatives. If one imagines a single "bare particular," one could also leave out the term "particular," which refers to parts of a whole, and just speak of a "bare."

According to the concept of absolute identity, the world would be as if it were a nondimensional point. There would be no multiplicity of entities or substances, no properties, no relations, neither space nor time as external or internal differentiations. The weaker alternatives of the notion of identity--(1) to (5)--would be trivialized or perhaps even denied by the notion of absolute identity because they all assume internal differentiation and differentiation between each other. (10)

While the weaker forms of identity are frequently interpreted as relations, (11) this is excluded from absolute identity, not only verbally ("absolute" means "without relation"), but also per definitionem because every relation requires the difference between relation and relata (or at least one relatum in the case of identity) and therefore requires some internal differentiation. Interpreting absolute identity as relation would place the category of relation on a higher level of abstraction than absolute identity, and therefore lead to a completely different metaphysical understanding of the world. Such a relational understanding of the world is certainly possible and--as will appear at the end of this study--also more plausible as a description of reality than that of absolute identity. However, in order to discuss absolute identity properly, the latter must be separated from such a relational picture of the world.

The concept of absolute identity can be explained to a certain extent by using more concrete categories, such as a combination of an existential claim, a quantity claim, and the negation of a difference claim. We would now say: There exists a "bare"; there is only one "bare"; and within this "bare," which is the world, there is no differentiation, especially no differentiation between "substance" and "properties"--which means that they are identical. (12)

Nobody seems to have defended or even ever much discussed absolute identity, perhaps because of its seemingly obvious implausibility. Plotinus' "The One" does not exclude differentiations. (13) Medieval philosophers were interested in unity but obviously not in absolute identity, perhaps because they recognized that absolute identity would, like Spinozism, imply the denial of any difference between God and the created world. So, only God before creation might be regarded as absolutely identical, but that would be a God without qualities, a God without self-consciousness, a God without the ability and possibility to create. (14) Obviously the Christian image of God as Trinity would be impossible.

The beginning of Hegel's Science of Logic, with its notion of "being" ("Sein") as "undetermined immediacy" ("unbestimmte Unmittelbarkeit"), (15) might be thought to approximate the notion of absolute identity. But Hegel's double negation and identification of "being" with "nothing" already refers to an internal differentiation, which immediately emerges at the start of the dialectical process ("Werden").

The notion of absolute identity is also more radical than the most radical solipsism or any brain-in-a-vat skepticism because either of these presumes that the reflecting "I" or brain is internally differentiated with respect to its mental acts. Solipsism or brain-in-a-vat-skepticism additionally does not preclude the fact that, from an external point of view, there could be several centers of solipsistic world construction; however, from the perspective of any solipsistic perceiver, these would exist as a result of his or her internal projections. The notion of absolute identity also rules out Descartes's deceiving God (16) because the existence of such a deceiver presupposes the differentiation between deceiver and deceived.

I do not assume anybody could be so foolish as to believe that the world must really be conceived as absolutely identical. However, I do think that the discussion, critique, and exclusion of absolute identity as the ontologically strongest possible meaning of the notion of identity is an important and even necessary step before reaching a sustainable understanding of the most fundamental structures of our world. The reason is this: Nonabsolute identity plays a crucial role on a second and any following level of abstraction of our worldview. Even the big-bang theory of modern physics comes close to the notion of absolute identity in at least one respect. The starting point of the cosmological expansion and the ending point of its hypothesized reversal are both described as a state of unimaginably high density and space--time collapse. This state could be understood as an empirical and therefore incomplete approximation of physics to the worldview implicit in the constructive notion of absolute identity. (17)

To discuss and evaluate absolute identity fruitfully it seems useful to distinguish three alternatives: the linguistic possibility of the assertion, the mental possibility of the concept, and the ontological possibility and reality of absolute identity. Finally, as we shall see, a coherence-move seems warranted.

I

The linguistic possibility of absolute identity. The assertion of the absolute identity of the world is possible insofar as we can form a phonetic or written speech act which contains the sign sequence "absolute identity"--as has been done in this paper thus far, but difficulties begin to emerge as soon as we look at a syntactical dimension of the understanding of this sign sequence. We can of course utter and understand the term "absolute identity" in the subject or predicate place of a sentence; for example, in "Absolute identity is possible" or "The world is absolutely identical." However, if we do so we already assume a subject-predicate differentiation, and this contradicts in a performative sense the content of the absolute-identity claim. Thus we can use the term "absolute identity" within sentences only if we employ a syntax theory that performatively contradicts the very term we are trying to explain in content. To evade this difficulty we might then understand the notion of "absolute identity" solely as a singular sign like "Wow!" Yet according to semiotics even such singular signs cannot be employed without a differentiation between this sign and other signs.

A similar performative contradiction emerges on the level of pragmatics. If one understands absolute identity as singular exclamation, this exclamation is only understandable as referring to some other speech act. So even this understanding of the sign sequence "absolute identity" contradicts the notion of absolute identity in a performative sense of contradiction.

On the level of semantics similar difficulties occur: Every referential connection of "absolute identity" to an extralinguistic world already implies an internal differentiation between language and extralinguistic world, and therefore a performative contradiction between the fact of reference and the worldview it refers to. If language contains a reference in any form to a language-independent reality, absolute identity could not be a proper object of that reference. This holds already for the subsentential level of words. The word "absolute identity" (if one conceives it as one semantically understood word) could correspond to no proper object without contradiction. Furthermore, the sentence "The world is absolutely identical" could correspond to no truth-making fact because the relation of sentence and fact already presupposes a differentiation. However, even if truth is not understood as a sentence--fact correspondence but rather in the terms of the coherence theory, it still demands some internal differentiation.

Therefore, "absolute identity" can be uttered as a phonetic or written speech act, but it cannot be claimed as being either true or false because there is a performative contradiction between the necessary syntactical, pragmatic, and semantic assumptions for a truth-functional claim and the content of the claim. So, any attempt to claim absolute identity is doomed to fail.

II

The mental possibility of absolute identity. Provided that it is possible to distinguish between language and thought, one could inquire not only into the linguistic but also the mental possibility of the notion of absolute identity. In order to do this, one should first investigate whether the concept of absolute identity is not already internally contradictory in the same sense that the concept of a "round square" or a "married bachelor" is internally contradictory. A way to conceive of such an internal contradiction would be the following: If the notion of identity necessarily presupposes the notion of relation, and if the attribute "absolute" is incompatible with the notion of relation--as we saw above--then attributing "absolute" to the notion of identity has the same contradiction-making consequences as attributing round to the notion of square. If we concede that "absolute" and "relation" are inconsistent with each other, this objection leaves us with the assumption that the notion of identity is necessarily a relation. So here again, the crucial question becomes: Is identity necessary and therefore in all its variations a relation? Arguably this is, at the very least, less clear for identity than it is for the square's squareness.

A first main objection is this: Even for numerical identity the attribute of "relation" appears to be rather anomalous because our normal expectation for at least two ontological, mental, or at least linguistic-referential distinct relata is not fulfilled. And the only uncontroversial qualifications for the identity-relation of a numerically identical object with itself are logical ones--reflexivity, symmetry, and transitivity--which can be assumed to be also due to identity itself. Leibniz's Law can be seen as an attempt to further qualify the sort of relation in which a numerical identical object stands to itself. However, that attempt is disputed, as everybody knows.

A second main objection is this: If one would assume that identity is necessarily relational, the notion of relation would be more abstract than the notion of identity because certainly not all relations are identical. But the assumption that the notion of relation is more abstract than the notion of identity would be not only ontologically and conceptually crucial but also questionable. So it is not at all clear that the notion of identity implies the notion of relation. It seems to be at least possible to build up a worldview in which the notion of relation is not more abstract than the notion of identity, but then we cannot assume that the compositum "absolute identity" is internally contradictory from the start, as "round square" is.

This leads to the third main objection: The qualification of a concept as "internally-mentally contradictory" requires more than mere doubt. It requires certainty beyond reasonable doubt. It bears the burden of proof. Otherwise it would no longer be a value-neutral qualification of concept relations. It would be a normative restriction of our thinking. It would strangle mental productivity. However, we might well doubt this in the case of the assumption that identity is necessarily relational. Wittgenstein denied that identity is a relation, and he found some followers. (18) We do not consider it as repugnant to think about absolute identity as to think about a round square--otherwise there would not be a paper about this subject exceeding the length of one line and no reader would have read this far. Therefore, we cannot assume that the notion of absolute identity is internally contradictory.

The qualification of the notion of absolute identity as not internally contradictory holds, at least if one allows concepts or thoughts that are internally not differentiated, that is, those that resemble basic concepts. Otherwise, the requirement that thoughts be internally differentiated would imply a contradiction between this thought and the content of the concept employed in it. There is a price to pay for the solution that assumes absolute identity as internally nondifferentiated concept or thought: The move blurs the difference between thoughts (propositions) and concepts. But the move is not logically precluded, although it does seem to be highly unacceptable from the perspective of any philosophy of mind. The concept of absolute identity would require absolute uniqueness. Thus, it would lead to a radically reduced understanding of the mental sphere. For example, we could not err about absolute identity or take a skeptical attitude towards it because error and skepticism must be related to something else and thus assume internal differentiation. This view would additionally require that the unique concept of absolute identity not represent or refer to an external world. So, it would necessarily lead to a very strong version of idealism, a version of idealism which also denies any difference between the thinking entity and its thoughts.

If one does not assume an idealistic understanding of thought, then one should allow concepts and thoughts to be in some way connected (for example, representationally) to an external world. However, this connection to an external world makes the concept of absolute identity already self-contradictory in content, because there is a difference between concepts and world.

Our result so far is that absolute identity is mentally possible only in the very radical form of one-concept idealism; however, this cannot be meaningfully claimed--only uttered.

Yet, what if language and thought were irrelevant--if, for example, there were no human beings who talked and thought? Could the universe be or become absolutely identical (in some final cosmological contraction)?

III

The ontological reality and possibility of absolute identity. The final questions are: Is absolute identity real? (19) Is absolute identity ontologically possible? In other words: Is the world absolutely identical or could it be?

Linguistic and mental difficulties aside, one might conceive of the first question as the ontological question because if its answer were "yes," every question concerning ontological differentiations, concerning substances, their qualities, and so forth would immediately be answered in the negative. The question seems to be even more fundamental than Leibniz's famous question: "Why is there something rather than nothing?" (20) because the "Why" already presupposes some sort of differentiation between cause and effect, for example, in the differentiation between God and world proposed by Leibniz, which is actualized by God. Even if one omits the interrogative-pronoun "Why," the question of absolute identity would be at least as important as Leibniz's question, for--as we will soon see--if absolute identity were real, "something" and "nothing" would be indistinguishable.

Is absolute identity real? The answer depends on how we understand the notion of reality. If one assumes with Frege that "existence" is a second-level predicate referring to a second-level concept, the answer is straightforward: The notion of second-level predicates and concepts presupposes sets. Sets are internally differentiated, even the zero set. So, the world cannot be absolute identical.

If one tries to employ a less logical and more ontological understanding of existence, we have to ask what the implications of this understanding are. One possibility would be to require at least reality in time and space (or in spacetime). But if we would conceive of absolute identity as real in that spacetime-sense, we would deny it immediately. A spacetime understanding of existence excludes absolute identity because absolute identity cannot admit the difference between objects and spacetime. Therefore, absolute identity cannot be assumed as real in any sense of being in spacetime. The same holds for other "thick" understandings of existence, for example, as consisting of a sort of substance in differentiation to mere properties. Even if one only demands that there are differentiated parts of an otherwise undifferentiated matter or material stuff, a res extensa, which builds up the world, absolute identity would be denied. So, no "rich" understanding of existence can be used to underwrite the reality of absolute identity. Absolute identity can be real only in a very "thin" sense of "being there," but then it seems to be impossible or at least very difficult to distinguish it from "something" or "nothing" being there. Just as a black hole absorbs all the light, absolute identity sucks every form of somethingness and nothingness into itself.

If absolute identity could be real only in such a thin understanding, we could deny its reality with a very high grade of probability. We have only to assume that the world consists of parts, of things and properties, or of time and space. The only possibility is to conceive of absolute identity as the unique abstract, idealistic being mentioned in II above. However, that alternative is so contrary to the worldview depicted by modern physics and so counterintuitive to our common-sense experience that we obviously have no reason at all to endorse it.

This raises the question: Is absolute identity at least possible? Could it be someday that the universe contracts to a point of absolute identity? Like existence, the ontological possibility of absolute identity depends on our understanding of "possible." If "possible" is understood as objective, it requires a differentiation between different possible worlds, different possible states of affairs or at least different possible properties of objects. Yet such an understanding contradicts absolute identity because it presupposes differentiations. If "possible" is understood as subjective, the differentiation between subject and object is incompatible with absolute identity.

So, like actual existence, absolute identity can be conceived as possible only in a very thin understanding as "maybe being there." The universe might, after the possible reversion of its ongoing expansion, contract to an absolutely identical point without differentiations (although mathematicians in a Platonistic mood might insist that even then abstract objects like points and classes continue to exist). This result would fit the notion of absolute identity as one idealistic concept. (21)

There is a problem with positing this possibility of our world contracting and becoming absolute identical. If one assumes that a world which is not absolutely identical contracts to an absolutely identical world, one has to presuppose change and therefore time. However, the assumption of such a change in time and therefore time itself is incompatible with the assumption of absolute identity. So, the change from a nonabsolutely identical to an absolutely identical state of the world seems to be impossible. If we acknowledge that our actual world is not absolutely identical, we could exclude the possibility that it might become absolutely identical in the sense that even time is ruled out as differentiation. It might become very dense in space, but it cannot become timeless. If time and space are related as the special and general theories of relativity in physics claim, the character and the flow of time might change drastically. Nonetheless, the past cannot be ruled out.

Even if we acknowledge that our actual world is not absolutely identical, with these arguments we could certainly not exclude the possibility of its becoming so. In that case, our actual word is already absolutely identical. So, the possibility of absolute identity is trivial if we assume that every actuality implies possibility. However, one could question if absolute identity would not rule out this implication in principle because it is not clear what the state of possibility could be, if it is identical with the state of actuality.

IV

A Coherence-Move. If the notion of absolute identity could be evaluated as real or unreal (or as possible or impossible) only in a very thin sense, that might be a reason to change our picture totally. Think of the very abstract forces of physics like gravity. It seems to make very little sense to say the law of gravity "exists." (22) The main quality or function of gravity seems to be not to exist but to force, to be effective.

This is the case inspite of the fact that physicists search for the "gravitron" as a particle. Perhaps the situation is similar with absolute identity. At this highest level of abstraction in our system of concepts and beliefs, the qualification "existent" is not decisive anymore, but the function of coherence is. It is similar to high-end physics. The differentiations begin to blur such that "existence" and "function" can no longer be distinguished.

In that case, how does "absolute identity" as a notion fare in respect to coherence-functionality? How would we relate such different notions as being and nothing? I think "absolute identity" does very badly in this respect. Absolute identity is captured in itself. It cannot reach out. It cannot relate and connect. So, we have a last and finally conclusive reason to reject absolute identity as an adequate concept of our world.

It has to be emphasized that this lack of functionality holds only for absolute identity at the most abstract level of our worldview. It does not hold for all forms of nonabsolute identity, conceived as relativity or relation, mentioned at the beginning of this paper. On the contrary, nonabsolute identity seems to be essential to the coherence of the world on any second or further levels of abstraction. Think of mathematics as mainly consisting of equations implicitly using nonabsolute identity. Think of science questioning in what respect particles, fields, or genes are identical. Think of personal identity as an essential concept for conceiving of ourselves. Think finally of our day-to-day questions regarding who is identical with whom and what is identical with what.

V

Some conclusions. What follows from this denial of absolute identity as an adequate conception of the world? There are three main consequences: the first one is limited to the weaker notions of identity, the second concerns the employment of identity in general, and the third very fundamental one involves our understanding of the world.

The first consequence has to be drawn with respect to the weaker forms of identity mentioned at the beginning. These weaker forms of identity are possible or at least, are nontrivial only if absolute identity is denied. So, in respect to the notion of absolute identity every one of these weaker notions necessarily includes some form of nonidentity, namely, some form of difference and/or relation. (23) Identity of quality presupposes the difference between two objects, if such identity should be distinguished from numerical identity. It further pre-supposes the relation of the two identical qualities of these objects (whether this relation be conceived as realistic or nominalistic, as internal or external). Relative identity and Leibniz's Law presuppose a difference between the identity of qualities and numerical identity, as well as a relation between objects and qualities. All identity presupposes some internal difference of mode and attribute within some unique substance and a relation between that substance and its modes and attributes. Even numerical identity would become indistinguishable from absolute identity, if we could not assume different numerically identical objects. Indeed, many assume numerical identity to be a sort of relation, although it is certainly a very anomalous one without a plurality of relata.

Thus, these weaker forms of identity cannot be built up solely from a concept of identity understood as absolute identity. Identity must be employed as one of the most important principles of our world, but it is limited and not absolute. It is relativistic. It must always be combined with some sort of relation and/or difference, and as we saw in the alternative notions of identity (1) to (5): The difference makes the difference.

A second more general consequence might frame the status of identity in the following abstract way: Although absolute identity has to be refused on the most abstract level of our picture of the world, that it is at least a serious candidate for this most abstract level establishes identity as one of the most important principles on the second and all following levels of abstraction in our worldview. To put it the other way round: Being so important and pervasive on all levels and in all different respects of our worldview makes identity in the form of absolute identity a serious, though not successful, candidate for the most abstract characterization of our picture of the world. Pervasive significance for the second and all following levels and the status as a serious candidate for the first level are two sides of the same coin. As in a music contest, being a very serious candidate for the first prize probably earns the candidate the second or third prize.

So, although our judgment concerning absolute identity was negative, the effort was not at all worthless. By scrutinizing absolute identity we have at least shown the seriousness of identity as a candidate for the first level of abstraction. Further, we have established an argument--and perhaps the best argument besides pure description--for considering identity as a basic principle for constructing our worldview on the second and all following levels.

The third most fundamental consequence of our considerations is this: If we deny the reality and especially the functionality of absolute identity, we exclude one very significant way to understand our world. For the world must then consist in at least two distinct beings (understood in a wider sense to refer also to space and time), which might even turn out to be an internally distinct, Spinoza-like, single, and unique substance. From this follows the question as to how these at least two distinct beings and their relation to each other have to be conceived. Do they stand in absolute difference to one another, or must we assume some form of relation? To put it in terms of the coherence-move: The function of ultimate coherence of the universe must be employed by another functional concept or principle. But by which? (24)

University of Gottingen, Germany

(1) If the same thing cannot be both F and not F or if it either has some property F or lacks it, we necessary presuppose "the same thing." See Colin McGinn, Logical Properties (Oxford: Clarendon Press, 2000), 11.

(2) An example: Somebody reserves a desk in a furniture store. When she comes by to fetch it, the storekeeper says: "Unfortunately one of my employees sold the desk I reserved for you. But I'll give you another identical one." Being the desk in a certain place, in a certain time, and so forth, turn out to be irrelevant properties in this case.

(3) When the reserved desk is not sold, and she asks if it is the one she reserved, the storekeeper answers: "This desk is identical with the desk I reserved for you yesterday." Numerical identity is already mentioned by Aristotle, Topics 1.7.103a7-14. Numerical identity is formalized as "x=y." "x=x" characterizes the reflexivity of numerical identity. Wittgenstein questioned the sense of the identity sign, because numerical identity can be expressed by using only one name, numerical difference by using two different names, Tractatus logico-philosophicus 5.53-5.534. See Roger White, "Wittgenstein on Identity," in Proceedings of the Aristotelian Society 78 (1977-8); and Christopher J. F. Williams, What is Identity? (Oxford: Clarendon Press, 1989), 15.

(4) See Peter Geach, "Identity," Review of Metaphysics 21 (1967): 3-12; Nicholas Griffin, Relative Identity (Oxford: Clarendon Press 1977); and Harry Deutsch, "Relative Identity," in Stanford Encyclopedia of Philosophy, 2002, available at http://plato.stanford.edu/entries/identity-relative/. Geach maintains in his article also that numerical identity alone is impossible and always needs a completion by a count noun. He seems to suppose that this claim and the denial of Leibniz's Law are identical, but that is questionable. One could very well acknowledge statements like "x=x" and "x=y" but reject Leibniz's Law.

(5) Identity of indiscernibles: ([for all]F) (Fx [left and right arrow] [for all]Fy) [right arrow] [for all]x=y; Indiscernibility of the identicals: x=y [right arrow] [for all] ([for all]F) (Fx [left and right arrow] [for all]Fy). Sometimes only the first or the second part is called "Leibniz's Law." See for the first: Max Black, "The Identity of Indiscernibles," in Mind 61 (1952): 153-164. For some problems of Leibniz's Law: Griffin, Relative Identity, 2. Some might argue that the indiscernibility of identicals is already expressed by the understanding (2) so that alternatives (2) and (4) would at least partially converge. However, I think one should differentiate the alternatives in order not to presuppose the discussion between (3) and (4).

(6) Parmenides, in The Presocratic Philosophers. A Critical History with a Selection of Texts, vol. 2, ed. Geoffrey S. Kirk, John E. Raven, Malcolm Schoefield (Cambridge: Cambridge University Press 1983), 249-50; Hermann Diels, Die Fragmente der Vorsokratiker, 6th ed., ed. Walther Kranz (Zurich: Weidmann, 1992), vol. 1, DK 28, B8, p. 235. Spinoza, Ethica, Pars 1, Propositio 5 and 14, in Spinoza, Opera II, 2nd ed., ed. Carl Gebhardt (Heidelberg: Winter, 1972). See for a general treatment of different forms of monism: Peter van Inwagen, Metaphysics (Boulder: Westview Press 1993), 28.

(7) Spinoza, Ethica, Pars 1, Definitio 4-5, Propositio 1, 2, 4, 5, 9-12.

(8) The one is thought as being continuous ([TEXT NOT REPRODUCIBLE IN ASCII])

(9) Francis Herbert Bradley, Appearance and Reality. A Metaphysical Essay, 9th ed. (Oxford: Clarendon Press, 1930), 125.

(10) The difference between trivialization and denial depends on the question whether or not it makes sense to speak of the identity of qualities or numerical identity if there is no differentiation between qualities and things. The denial holds for alternative (5) of all-identity only if it is conceived as demanding a sort of internal differentiation and not only allowing it.

(11) See David Hume, A Treatise of Human Nature, ed. L. A. Selby Bigge and P. H. Nidditch (Oxford: Clarendon Press, 2nd ed. 1978), bk. 1, part 1, [section] 5, p. 14; Charles Sanders Peirce, Collected Papers, eds. Charles Hartshorne and Paul Weiss (Cambridge, Mass.: Belknap, 1965-), vol. 1, p. 461; McGinn, Logical Properties, 12-14. Wittgenstein refused this understanding of identity as relation, in Tractatus logico-philosophicus 5.531. See Roger White, "Wittgenstein on Identity," in Proceedings of the Aristotelian Society 78 (1977-8). Williams defends this view. What is Identity? 15.

(12) What might be an attempt to give a formalization of absolute identity? [there exists]x[for all]y (x=y) would not do because it only requires monism (Spinozism), that is, it demands one and only one entity, but does not exclude properties. Applying the law of indiscernibility of the identical, [there exists]x[for all]y (x=y) [right arrow] [for all] [for all]F) (Fx [left and right arrow] [for all]Fy), would not help because it excludes a multiplicity of properties, but allows one and only one property of the one and only entity. So, we have to exclude that the one and only one entity has a property: [there exist]x[for all]y (x=y) [conjunction] [for all]F[for all]x-Fx.

(13) Plotinus, The Enneads, ed. John Dillon, trans. Stephen MacKenna (London: Penguin Books, 1991), Ennead 5, treatise 1, chap. 10. Plotinus assumes so called "hypostases." Upon the One follows the principle of Being, the principle of the Intellect, and the principle of the Soul.

(14) While Thomas Aquinas assumed that God is simple and has no accidents, that does hot mean that He has no properties, see Eleonore Stump, Aquinas (London: Routledge, 2003), 112.

(15) Georg W. F. Hegel, Wissenschaft der Logik, Vol. 5, eds. Eva Moldenhauer and Karl M. Michel (Frankfurt/Main: Suhrkamp Verlag, 1969), 82.

(16) Rene Descartes, Meditations, ed. Desmond M. Clarke (London: Penguin Books, 1998), 20.

(17) See Brian Greene, The Elegant Universe. Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory (New York: Vintage, 2003), 83, for a description of the classical big-bang theory: "And as the clock is turned back to ever earlier times, the whole of the cosmos is compressed to the size of an orange, a lemon, a pea, a grain of sand, and to yet tinier size still. Extrapolating all the way back to the 'beginning', the universe would appear to have begun as a point ... in which all matter and energy is squeezed together to unimaginable density and temperature." See p. 235: "[F]rom a maximum size of many billions of light-years, the universe will shrink to millions of light-years, every moment gaining speed as everything is crushed together to the size of a single galaxy, and to the size of a single star, a planet, and down to the size of an orange, a pea, a grain of sand, and further, according to general relativity, to the size of a molecule, an atom, and in a final inexorable cosmic crunch to no size at all." But string theory assumes that the universe has Planck-size, that is Planck-length in all dimensions, in the state of the big-bang and the possible big crunch. See also pp. 254, 350, 366.

(18) See footnote 11.

(19) "Real" and "existent" will not be distinguished here.

(20) G. W. Leibniz, "On the Ultimate Origination of Things," in Philosophical Writings, ed. G. H. R. Parkinson (London: J. M. Dent and Sons, 1973), 136-44. See Arthur Witherall, The Problem of Existence (Aldershot: Ashgate, 2002).

(21) See section II above

(22) However, it is worth remembering that modern physics assumes some sort of "force particles": gluons for the strong force, photons for the electromagnetic force, weak gauge bosons for the weak force, and gravitons for gravity. Only the weak gauge bosons are thought to have a mass. So, how can we suppose that a particle exists if it has no mass? Further, how are we able to distinguish forces with their particles from quarks as "forceless" particles?

(23) I follow Hume in denying that difference is a relation. See Hume, A Treatise of Human Nature, 1.5, p. 15. Aristotle already distinguished forms of difference which are relations and others which are not: Categories 2.9.11b16.

(24) I wish to express my gratitude for very helpful suggestions to Pierpaolo Ciccarelli, Lydia Goehr, Holger Gutschmidt, Georgios Karageorgoudis, Linda Peer, Tobias Rosefeldt, David I. Seipel, and Achille Varzi.

Correspondence to: Lehrstuhl fur Rechts- und Sozialphilosophie, Platz der Gottinger Sieben 6, D-37073 Gottingen, Germany.
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Author:Von Der Pfordten, Dietmar
Publication:The Review of Metaphysics
Article Type:Report
Geographic Code:1USA
Date:Jun 1, 2009
Words:6179
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