Notes 1 Introduction 1. The term (logischer Raum in German) “originates in Boltzmann’s general- ized thermodynamics, which treats the independent properties of a physical system as defining separate coordinates in a multidimensional system the points of which constitute the ‘ensemble of possible states’” (Hans-Johann Glock 1996: 220). 2. One might object here (as, indeed, an anonymous referee did during the book proposal submission stage) that recent speculative theories in physics, like Max Tegmark’s mathematical universe (or great ensemble theory), and, more generally, multiverse theories are examples of scientists dealing with logical space at the most fundamental level. However, this objection is misguided. The multiverse is not the same as a logical space; the multiverse is a hypoth- esis about the actual world, namely that it contains many spatio-temporally and causally disconnected universes. One can conceive of other worlds where there is no multiverse, but only one universe. This is obvious by the very fact that the multiverse is a hypothesis, which, for all we know, could be true or false. It must then be the case that there are open epistemic possibilities corresponding to whether the world is a multiverse or a universe. So the multiverse or the “great ensemble” is simply not enough to serve as a logical space. Also, there is virtually no discussion even in these highly speculative approaches in theoretical physics about the nature of modality, possible worlds, and so on. 3. Tractatus, 3.42: “A proposition can determine only one place in logical space: nevertheless the whole of logical space must already be given by it. (Otherwise negation, logical sum, logical product, etc., would introduce more and more new elements in co-ordination.)” 4. The original is “the mind and the world jointly make up the mind and the world”, and is a slogan for Putnam’s “Internal Realism”. See Putnam 1981: xi. 5. Although at the 2011 annual conference of the British Society for Philosophy of Religion, I learnt from Yujin Nagasawa that while I was working on this book, he was developing the very same view in a manuscript titled “Modal Panentheism”. I have read the paper and there are several ideas that I share with Yujin, and they are argued for in this book. 2 What Is Logical Space? 1. These examples were put forward to me as alleged counterexamples to logical totalitarianism by Ezgi Ulusoy Aranyosi and Ralf Bader. 2. This sentence was raised as a challenge to logical totalitarianism by Ilhan Inan. 181 182 Notes 3. The polarity of a state of affairs indicates whether the relations hold or not for the constituent objects. 4. Thus situation theory is also an alternative to the Fregean view that the semantic value (or reference) of a sentence is its truth-value. 5. To which the constraint of consistency is added, that is, that there is no world at which (P & ¬P) is true, thus the standard definition of “possible world” is that of a maximal consistent set of sentences (or propositions). 6. For details, see Zalta 1993. 3 “Life” in Logical Space 1. If unknowingly, for example because of split personality, you are writing a letter to yourself, then you are not a fictional character, so, again, the letter is self-undermining. 2. For the Russellian-Quinean the only truth about Pegasus is “Pegasus does not exist”, whereas Meinongians can assert sentences like “Pegasus is fictional”, “Pegasus is mythical”, and so on. This is one reason Meinongians fare better in accommodating the intuition that all these sentences are true or assertible. On the other hand, Meinongians would go further and also assert sentences like “Pegasus is a winged horse”, with respect to which, according to some philosophers, intuitions are indeterminate. 3. See Bernard Linsky and Ed Zalta 1991. 4. For a more elaborate treatment of this idea and, in my view, a devastating criticism of Routley’s claims to parsimony and novelty of his approach, see Lewis 1990b. 5. For the orthodox Russellian-Quinean view, see W.V.O. Quine 1948. For various Meinongian views, see Alexius Meinong (in Roderick Chisholm 1960), Routley 1980, Parsons 1980, and Zalta 1983. For Lewis’ view, see his 1986. 6. An exception is Takashi Yagisawa (2010), whose notion of existence at an index can be relative to a domain, to a time, to a place, and to a world. The relativity I propose here, as well as the argument for it, are different from Yagisawa’s. 7. As Jaakko Hintikka (1962) has pointed out, the argument is not really an inference in the classical sense, but a performance, that is we are supposed to perform its steps on ourselves in order to realize its force and soundness. 8. The fallacy is to deduce some proposition P from [(P implies Q) and P]. 9. Several people insisted, whenever I presented these ideas at various confer- ences, that if we are real, then we are not fictional, as a matter of analysis (for instance, Howard Robinson, Nick Effingham, and others). I disagree. In light of my arguments presented above, the notion of fictionality is also a rela- tive one. And so is that of reality. For instance, Sherlock Holmes is fictional relative to our world, but real relative to the world our fiction depicts him as being present in. There is also a related criticism or proposal, namely, that an object is fictional only if it is an actual nonconcrete object. My notion of Logical Space, of course, allows such a view, that is, such a view has a place in some logical region, but it is not a constraint on that space at all. Sherlock Holmes is a bona fide object in virtue of its so-sein. At a logical region that depicts Sherlock Holmes as a nonconcrete object (which means that it does not Notes 183 instantiate properties like being a detective, being smart, and so on), Holmes’ so-sein is perhaps the set of properties: {being nonconcrete, encoding the property of being a detective, encoding the property of being smart, and so on}. Although the first of these properties are, for Meinongians, paradigmatic extranuclear properties, and all of them except the first one are also higher-order, the notion of Logical Space and the doctrine of Logicalism proposed here makes it the case that they are all treated on a par, as nuclear, or so-sein making properties. 10. Meinong also posited such objects as inhabitants of his ontology. Objects of intentional states as well as certain uınderspecified, generic objects such as “the triangle”, are in this category. For Meinong these objects are determined by the properties that explicitly figure in their depiction. So the triangle is an incomplete object determined by triangularity, the isosceles triangle is determined by triangularity and being isosceles. 11. This is not to say that whenever two expressions have the same sense, the identity statement that they flank is trivial; a counterexample is the case of synonyms, because arguably an identity statement containing synonyms as its terms is not trivial, though it is a priori knowable. 12. One could object that, still, it is because of Carew’s knowledge and verbal dispositions dependent on it that substitution fails. However, it is not true that Carew would accept “Dr. Jekyll is trustworthy and friendly” and reject “Mr. Hyde is trustworthy and friendly”; he simply has no knowledge or any attitude towards the propositions regarding Dr. Jekyll and Mr. Hyde. 13. I adopt here what Thomas MacKay and Michael Nelson (2010) regard as the metaphysical conception of de re attitude. See their article for the syntactic and the semantic conception. 14. There is actually more to it, in this particular case, than the fact that the objects are named as they are, namely, the name “Superman” connotes some property like being a superior human, or something similar. To assert that it is only the way they are named that is relevant to attitude ascriptions involving some intentional objects appears to be liable to the criticism Frege – in the first paragraph of “On sense and reference” – adduced against the view that identity is to be understood as a relation between signs, which wouldn’t explain the informativeness of some identities. 15. I owe the phrase “gentrification of logical space” to Nicholas Silins. 4 Folded Logical Space 1. The notion of the definition of a situation would come to play a funda- mental theoretical role in a very influential school of thought in sociology and anthropology – Symbolic Interactionism – with applications in various subfields of these disciplines. George Herbert Mead, a key theorist of symbolic interactionism, who was a colleague of Thomas at the University of Chicago, expressed a thesis similar to the Thomas Theorem: “If a thing is not recog- nized as true, then it does not function as true in the community” (Mead 1936: 29). 2. The case that Merton made popular, namely, the self-fulfilling prophecy, implies or requires, therefore, strictly speaking, more than what the Thomas 184 Notes Theorem does. It requires not only that what is defined as real be real in its consequences, but also that it become real per se, or real in its causes. Another such example of something becoming real per se as a result of people defining it as real is the entity we call “nation”. Benedict Anderson’s seminal book on nationalism (1983) makes this clear when Anderson asserts that although the nation is an imagined community, it does not mean that it is fabricated (1983: 6); by being imagined by a sufficiently high number of otherwise spatially disconnected people who never get a chance in their lives to interact face-to-face, the nation comes to be realized, or comes into existence.