Possible Worlds (Stanford Encyclopedia of Philosophy). Although . In addition to the usual sentence operators. Although a prominent aspect of logic in both. Aristotle's work and the work of many medieval philosophers, modal. And even though a variety of modal deductive systems had in. I defend the compatibility of actualism – i.e. 5 Actualism and Possible Worlds Source: Essays in the Metaphysics of. Ontological Commitment, and Possible World. Actualism, Ontological Commitment, and Possible World Semantics Christopher Menzel Here are some quotes representative. Actualism and Possibilism and Intensional Possible Worlds Given our two logistic systems HST and HST as formulations of Russell Actualism, Singular Propositions, and Possible Worlds: Essays in the Metaphysics of Modality by Aviv Hoffmann Submitted to the Department of Linguistics and Philosophy on September 6, 2002 in Partial Fulfillment of the. ALAN McMICHAEL A NEW ACTUALIST MODAL SEMANTICS 1. A PROBLEM FOR ACTUALISM ABOUT POSSIBLE WORLDS Suppose that we interpret necessity as truth in all possible worlds, possi- bility as truth in some possible world. Keywords possible worlds; combinatorialism; actualism; possible world semantics; Transparent intensional logic. Possible worlds are systems of possible outcomes of applications of procedures collected in. Issue published online. Actualism, Singular Propositions, and Possible Worlds: Essays in the Metaphysics of Modality by Aviv Hoffmann BA Philosophy The Hebrew University of Jerusalem, 1993 SUBMITTED TO THE DEPARTMENT OF LINGUISTICS AND PHILOSOPHY IN. Softcore actualists agree with pos-. Actualism and possible worlds. ALVIN PLANTINGA; Article first published online. Get PDF (1005K) Get PDF (1005K) More content like this.Lewis and Langford (1. Tarski had. provided for the languages of classical first- order. Consequently, there was no rigorous account of what it means. A concomitant philosophical casualty of. Quine, toward any appeal to modal notions in. The extension of a denoting expression, or. By contrast, the intension of an expression is. For purposes here, let us say that a. An extensional logic. A substitutivity principle says that, if two. Modal logic, by. contrast, is intensional. To illustrate: the substitutivity principle. So suppose that. John's only pets are two dogs, Algol and BASIC, say, and consider two. English counterparts): All John's dogs are mammals: . All John's pets are mammals: . Hence, in. accordance with the classical substitutivity principle for sentences. Not all John's dogs are mammals: . In a modal logic that accurately represents the. For, according. to our example, the predicates . However, while. substituting the latter predicate for the former in (3) results in a. Absent a rigorous semantic. Standard model theoretic semantics for the. Tarski (1. 93. 3. Given these. assignments, sentences are evaluated as true under the interpretation I — true. I, for short — according to a more or less familiar set of clauses. To facilitate the definition, let I. In particular, where. An existentially quantified sentence. From Tarskian to Possible World Semantics. The truth. conditional clauses for the three logical operators directly reflect. For a Tarskian interpretation fixes the domain of. Pretty. clearly, however, to capture necessity and possibility, one must be. For, intuitively, under different circumstances. A bit more formally. Both the domain of quantification and the extension of the. Also as in Tarskian. M assigns each term . Say that M is the. Then, where M. is the intended interpretation of . Hence, if w is a world where John has a pet. COBOL, say — COBOL is in the w- extension. Since, semantically speaking, the necessity. For, unpacking the right side of. Thus, spelling out the negation. Summary: Intensionality and Possible Worlds. Analyzed in terms. Their syntactic similarity to. The possible worlds analysis of. When the modal operators are interpreted as. That the truth values of. Possible world semantics, therefore. Spelled out as. possible world truth conditions, those meanings can be expressed in a. Of course, the semantics of. Two particularly important. As much a barrier to the. It is a virtue of possible world. More specifically, as described above, possible. We can define. an intension per se, independent of any language, to be any. More specifically. A proposition is any function from worlds to truth. This reply appears. The De Re / De Dicto Distinction. A particularly. rich application of the possible world analysis of intensions. Thus, for. example, intuitively, John's dog Algol is a pet accidentally; under. But she is a dog essentially; she couldn't have. Likewise. a has F accidentally if a has F in the. Modal sentences that do not, like. Necessarily, all dogs are mammals: . More specifically, basic possible. In this way, one and the. Unfortunately, the. Two arise with particular. What, exactly, is a possible world? Fleshed out philosophical accounts of this. A particularly powerful intuition is that situations are. Anne's office. — notably Anne herself, her desk and her computer, with her. On this view, for one situation s. The actual. world, then, as the limit of a series of increasingly more inclusive. Call this. the concretist intuition, as possible worlds are understood to. But, for the concretist, other possible worlds are. There are countless other worlds, other very inclusive. However, it is important to note that Lewis. Lewis writes, “that is good enough”. So with this caveat, let us say that that an. Then we have the following. AW1w is a possible world =defw is a maximal. The actual world does not enjoy a. Other worlds. and their inhabitants exist just as robustly as we do, and in. Thus, the. referent of . By. the same token, when we speak of non- actual possibilia —. Lewis's preferred label for the denizens of possible worlds — we. In the mouth of an other- worldly metaphysician, we. Modal Reductionism and Counterparts. Lewis parted ways dramatically. W. Lewis, by contrast, wholly embraces the objectivity of. What he denies. however, is that modality is a fundamentally irreducible. Lewis, that is, is a modal. For Lewis, modal notions are not primitive. Rather. truth conditions for modal sentences can be given in terms of worlds. Lewis claims, are defined. The earliest presentation of Lewis's. Lewis 1. 96. 8) — reflecting Quine's. Nonetheless, it is useful to. AE1, of. course), and the counterpart relation, which will be. Wx: x is a. world. Ixy: xexists in world y. Cxy: x is a counterpart of y. For sentences like. Lewis's truth conditions. For every world w, every individual x in. Also as in possible world semantics. However, unlike possible world. Rather, for Lewis, each. Thus, in particular, the. Likewise, the pet predicate. Such a move is not feasible in basic possible world semantics. Hence, a typical predicate will be true of an. But, for Lewis, as we've seen, distinct possible worlds do not. For. example, since Algol is in fact a pet, given worldboundedness and the. There is no world w such that Algol exists in. Hence, (1. 9) might appear to be exactly the. Lewis's. analysis, Algol is not a pet accidentally but essentially; likewise. His explanation involves one of the most. Roughly, an object y in a world. A typical other- worldly counterpart of Algol, for. John. Hence, sentences making de re assertions about. Algol might have done or what she could or could. Thus, when we analyze. Algol is a pet, but there is a world in which exists a. Ta . Lewis's possible world truth. Tarskian semantics. However. given worldboundedness and the fact that predicate extensions are. Lewis's. theory. As in basic possible world semantics, intensional entities in. And because individuals are worldbound, Lewis is able to. To the extent that these notions. Lewis has arguably reduced modal notions to. Significantly more controversial, and perhaps far. The truth condition. Algol is no one's pet. By virtue of what in Lewis's theory does such. The ideal answer for Lewis would be that some. Lewis 1. 98. 6, 8. From this it would follow that the. Toward this end, Lewis initially considers the. Ways. Absolutely every way that a world could be is a way. But there is a fatal flaw here: Lewis himself. So understood, Ways collapses into the triviality. The principle has two aspects. The first is the principle. For “if. there could be a dragon, and there could be a unicorn,” Lewis. Given that individuals are worldbound, however, the principle is. R1. For any (finite or infinite) number of objects. For. “if there could be a talking head contiguous to the rest of a. To express this a bit more. R2. For any world w any (finite or infinite number of). Hence, the existence of such worlds. Worlds containing talking donkeys, exotic species. Nonetheless, it is not entirely implausible to think such. For, as a realist about worlds, Lewis. Their role. therefore, is to give us insight into the richness and diversity of. Likewise recombination. Furthermore, because worlds. Lewis's translation scheme themselves appear. Hence, unlike many other popular. Lewis's promises to provide a. Lewis faces. this objection head on: His theory of worlds, he acknowledges. However, Lewis. argues that no other theory explains so much so economically. With. worlds in one's philosophical toolkit, one is able to provide elegant. As high as the intuitive cost is, Lewis (1. The theoretical benefits are worth it.”. Additional discussion of, and objections to, concretism can be found. Further Problems for Concretism. We can now. imagine, as in our example, further detail being successively added. Anne. working at her desk in her office; music being in the background; her. Roughly speaking, then, a possible world. Thus, for example, that things. The propositionthat Anne is in her office and. For purposes here, however, we will sketch the fundamentals. Plantinga. (1. 97. Lewis's. concretism. It is simply to say that it is not, in fact. So, henceforth, to express that an SOA is actual we. One SOA s is said to include another. So, for example, Algol's being John's. Algol's being someone's pet and precludes. Thus, on the abstractionist's. Finally, say that an SOA s is total if, for every. SOA t, s either includes or precludes t. Note also. that, for the abstractionist, as with the concretist, the actual. The actual world is simply the total possible SOA that, in. And non- actual worlds are simply those total possible. SOAs that do not. As we've seen, on Lewis's account. Clearly, because SOAs are abstract, individuals cannot. Accordingly, the abstractionist defines existence. AE2. Individual aexists in possible world. Indeed, typically, abstractionists are staunchly. The abstractionist, therefore, has no. AW2 and AE2). In particular. The reason for this is. SOA that (among other things). Hence, unpacked in terms. And spelling out those. Plantinga’s definition will. The logical framework of abstractionism is modal. Hence, if possible world semantics is supplemented. For the abstractionist can argue that the. The. reductionist wants to understand modality in terms of worlds; the. That is, the abstractionist can argue that we begin with a. Poss. The analysis that the. Nec and Poss fall out as. Plantinga 1. 98. 5 and Menzel and Zalta. Concretists define intensional entities in. This divergence in their choice of ontological primitives. The concretist is far more pragmatic; notions of. Lewis 1. 98. 6. 5. Within a given theory, any entities that can play those roles. Thus, Lewis finds it to be a strength of. By contrast, at least some abstractionists —. Plantinga (1. 98.
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