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.e., the causal relation does not take us to worlds that violate thelaws of our universe.The many-worlds interpretation of quantum mechanics,as described in chapter three, 6.2, provides an example of a multiverse thatvalidates S4 in this way.We will not attempt to decide here whether the appropriate modal logic forconceptual natural realism is S4 or S5.Instead, we will leave that decision tothe different variants of this ontology that might be developed.These variantsmight differ not only in respect of which modal logic is adopted, but also inwhether the first-order logic of the variant is possibilist or actualist, and alsowhether it allows for only a constructive conceptualism or a more comprehensiveholistic conceptualism.However, because S4 is a proper part of S5, we will useS4 here without assuming that S5 is thereby precluded.In regard to notation,5For an account of the different worlds in the multiverse, or megaverse, see Kaku 2005.6See Cocchiarella 1986, chapter III, 7, for an axiomatization and completeness theoremof natural realism based on this interpretation.7A model-theoretic approach to a causal modality would be based on an extension of thenotion of a causally extended system of world lines as described in chapter two for the causaltenses.At each node of such a causally connected system we would have not only the actualspace-time points of our universe that can be reached by a light signal, but also space-timepoints that are causally possible at that node as well. 280 CHAPTER 12.THE LOGIC OF NATURAL KINDSwe will use c for causal necessity and f&c for causal possibility.Now, instead of the ontological thesis of moderate realism (MR), we havethe following ontological thesis of modal moderate realism as a fundamentalprinciple of natural realism:("nFj)f&c("ex1).("exj)F(x1,., xj).(MMR)Natural properties and relations exist not as components of actual facts, inother words, as was stipulated in the thesis of moderate realism, but as thenexuses of possible states of affairs.It is in this sense that the being of anatural property or relation is its possibly being in re.There is no general comprehension principle that is valid in natural real-ism, incidentally, the way that the comprehension principle (CP" ) is valid forconceptual realism.Natural properties and relations are not formed, or con-structed, out of other properties and relations by logical operations.But thisdoes not mean that no natural property or relation can be specified in termsof a complex formula, i.e., a formula in which logical constants occur.What itdoes mean is that such a specification cannot be validated on logical groundsalone, but must be taken as a contingent hypothesis about the world.In order to consider specifying natural properties and relations in termsof complex formulas, it is convenient to have some abbreviatory notation.Inparticular, we can adopt some useful abbreviatory notation that simulates nom-inalizing predicates as objectual terms.We adopt for this purpose the followingnotation, which simulates a kind of identity between natural properties or rela-tions8:(Fj a"c Gj) =df c("x1) c.c("xj) c[F(x1,., xj) ! G(x1,., xj)]We say that a"c represents an identity between natural properties and rela-tions because, unlike concepts, natural properties and relations are identical when, as matter of causal necessity, they are coextensive.As part of the causalstructure of the world, natural properties and relations retain their identity as natural properties and relations across all causally accessible worlds.As part of nature s causal matrix, natural properties andrelations are identical when, as a matter of causal neces-sity, they are co-extensive.Now the assumption that there is a natural property or relation correspond-ing to a given predicable concept that is represented by a complex formula ,and hence by the -abstract [x1.xj], can be formulated as follows9:("nFj) c ([x1.xj] a"c F).8Only the initial occurrence of c is needed here if the presumed modal logic is S5.Theadditional occurrences are needed if the logic is S4.9With S5, instead of S4, this axiom can be stated simply asj("nF )([x1.xj] a"c F ). 12.4.ARISTOTELIAN ESSENTIALISM 281Here, we note again, that, unlike the comprehension principle of conceptualrealism, such an assumption is at best only a scientific hypothesis, and as suchmust in principle be subject to confirmation or falsification.In this regard, thereis no comprehension principle valid in natural realism other than the trivial onestipulating that every natural property or (j-ary) relation is a value of the bound(j-ary) predicate variables, i.e.10,("nFj) c("nGj)(F a"c G).12.4 Aristotelian EssentialismConceptual natural realism without natural kinds might be an adequate ontolog-ical framework for some philosophers of science; but to others, especially thosewho fall in the tradition of Aristotle and Aquinas, it is only part of a larger,more interesting ontology of Aristotelian essentialism.This is a framework thatis a part of cosmology as well as of ontology.It is part of cosmology because it isbased on natural kinds as causal structures, and it is part of ontology in that itdetermines two types of predication in reality, essential and accidental.Naturalkinds whether in the form of species or genera, and whether of natural kindsof things, such as plants and animals, or natural kinds of stuff , such as thechemical substances gold, oxygen, iron, etc., or compound substances such aswater, salt, bronze, etc. are the bases of essential predication, whereas predi-cable concepts and natural properties and relations are the bases of accidental,or contingent, predication.The basic assumption of this extension of natural realism is that in additionto the natural properties and relations that may correspond to some, but notall, of our predicable concepts, there are also natural kinds that may correspondto some, but not all, of our common-name concepts especially those that aresortals, i.e
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