Possible worlds

2018 ◽  
Author(s):  
Joseph Melia
Keyword(s):  
Modal Logic ◽  
Actual World ◽  
Possible Worlds ◽  
Abstract Objects ◽  
Causal Powers ◽  
Possible World ◽  
Space And Time ◽  
Wide Range ◽  
Concrete Objects

The concept of Possible worlds arises most naturally in the study of possibility and necessity. It is relatively uncontroversial that grass might have been red, or (to put the point another way) that there is a possible world in which grass is red. Though we do not normally take such talk of possible worlds literally, doing so has a surprisingly large number of benefits. Possible worlds enable us to analyse and help us understand a wide range of problematic and difficult concepts. Modality and modal logic, counterfactuals, propositions and properties are just some of the concepts illuminated by possible worlds. Yet, for all this, possible worlds may raise more problems than they solve. What kinds of things are possible worlds? Are they merely our creations or do they exist independently of us? Are they concrete objects, like the actual world, containing flesh and blood people living in alternative realities, or are they abstract objects, like numbers, unlocated in space and time and with no causal powers? Indeed, since possible worlds are not the kind of thing we can ever visit, how could we even know that such things exist? These are but some of the difficult questions which must be faced by anyone who wishes to use possible worlds.

Analysing Modality

2020 ◽  
pp. 22-73
Author(s):  
Alastair Wilson
Keyword(s):  
Actual World ◽  
Possible Worlds ◽  
Modal Realism ◽  
Possible World ◽  
Metaphysical Modality ◽  
Novel Theory ◽  
Reductive Theory

This chapter presents and defends the basic tenets of quantum modal realism. The first of these principles, Individualism, states that Everett worlds are metaphysically possible worlds. The converse of this principle, Generality, states that metaphysically possible worlds are Everett worlds. Combining Individualism and Generality yields Alignment, a conjecture about the nature of possible worlds that is closely analogous to Lewisian modal realism. Like Lewisian modal realism, Alignment entails that each possible world is a real concrete individual of the same basic kind as the actual world. These similarities render EQM suitable for grounding a novel theory of the nature of metaphysical modality with some unique properties. Also like Lewisian modal realism, quantum modal realism is a reductive theory: it accounts for modality in fundamentally non-modal terms. But quantum modal realism also has unique epistemological advantages over Lewisian modal realism and other extant realist approaches to modality.

Modal logic, philosophical issues in

2018 ◽  
Author(s):  
Thomas J. McKay
Keyword(s):  
Modal Logic ◽  
Natural Language ◽  
Possible Worlds ◽  
Possible World ◽  
Modal Claim ◽  
Knowing That ◽  
Modal Semantics ◽  
Bull's Eye ◽  
Modal Systems ◽  
Richard Montague

In reasoning we often use words such as ‘necessarily’, ‘possibly’, ‘can’, ‘could’, ‘must’ and so on. For example, if we know that an argument is valid, then we know that it is necessarily true that if the premises are true, then the conclusion is true. Modal logic starts with such modal words and the inferences involving them. The exploration of these inferences has led to a variety of formal systems, and their interpretation is now most often built on the concept of a possible world. Standard non-modal logic shows us how to understand logical words such as ‘not’, ‘and’ and ‘or’, which are truth-functional. The modal concepts are not truth-functional: knowing that p is true (and what ‘necessarily’ means) does not automatically enable one to determine whether ‘Necessarily p’ is true. (‘It is necessary that all people have been people’ is true, but ‘It is necessary that no English monarch was born in Montana’ is false, even though the simpler constituents – ‘All people have been people’ and ‘No English monarch was born in Montana’– are both true.) The study of modal logic has helped in the understanding of many other contexts for sentences that are not truth-functional, such as ‘ought’ (‘It ought to be the case that p’) and ‘believes’ (‘Alice believes that p’); and also in the consideration of the interaction between quantifiers and non-truth-functional contexts. In fact, much work in modern semantics has benefited from the extension of modal semantics introduced by Richard Montague in beginning the development of a systematic semantics for natural language. The framework of possible worlds developed for modal logic has been fruitful in the analysis of many concepts. For example, by introducing the concept of relative possibility, Kripke showed how to model a variety of modal systems: a proposition is necessarily true at a possible world w if and only if it is true at every world that is possible relative to w. To achieve a better analysis of statements of ability, Mark Brown adapted the framework by modelling actions with sets of possible outcomes. John has the ability to hit the bull’s-eye reliably if there is some action of John’s such that every possible outcome of that action includes John’s hitting the bull’s-eye. Modal logic and its semantics also raise many puzzles. What makes a modal claim true? How do we tell what is possible and what is necessary? Are there any possible things that do not exist (and what could that mean anyway)? Does the use of modal logic involve a commitment to essentialism? How can an individual exist in many different possible worlds?

Constructing the Impossible

2021 ◽  
pp. 141-163
Author(s):  
Kit Fine
Keyword(s):  
Natural Language ◽  
Possible Worlds ◽  
Formal Languages ◽  
Impossible Worlds ◽  
Possible World ◽  
Limited Role ◽  
Wide Range ◽  
Degree Of Acceptance ◽  
Broad Role ◽  
Natural Way

Please keep the original abstract. A number of philosophers have flirted with the idea of impossible worlds and some have even become enamored of it. But it has not met with the same degree of acceptance as the more familiar idea of a possible world. Whereas possible worlds have played a broad role in specifying the semantics for natural language and for a wide range of formal languages, impossible worlds have had a much more limited role; and there has not even been general agreement as to how a reasonable theory of impossible worlds is to be developed or applied. This chapter provides a natural way of introducing impossible states into the framework of truthmaker semantics and shows how their introduction permits a number of useful applications.

Modal logic

2018 ◽  
Author(s):  
Steven T. Kuhn
Keyword(s):  
Modal Logic ◽  
Possible Worlds ◽  
Predicate Logic ◽  
Modus Ponens ◽  
Possible World ◽  
Metaphysical Necessity ◽  
Truth Values ◽  
Classical Counterpart ◽  
Modern Development ◽  
Modal Predicate Logic

Modal logic, narrowly conceived, is the study of principles of reasoning involving necessity and possibility. More broadly, it encompasses a number of structurally similar inferential systems. In this sense, deontic logic (which concerns obligation, permission and related notions) and epistemic logic (which concerns knowledge and related notions) are branches of modal logic. Still more broadly, modal logic is the study of the class of all possible formal systems of this nature. It is customary to take the language of modal logic to be that obtained by adding one-place operators ‘□’ for necessity and ‘◇’ for possibility to the language of classical propositional or predicate logic. Necessity and possibility are interdefinable in the presence of negation: □A↔¬◊¬A and  ◊A↔¬□¬A hold. A modal logic is a set of formulas of this language that contains these biconditionals and meets three additional conditions: it contains all instances of theorems of classical logic; it is closed under modus ponens (that is, if it contains A and A→B it also contains B); and it is closed under substitution (that is, if it contains A then it contains any substitution instance of A; any result of uniformly substituting formulas for sentence letters in A). To obtain a logic that adequately characterizes metaphysical necessity and possibility requires certain additional axiom and rule schemas: K □(A→B)→(□A→□B) T □A→A 5 ◊A→□◊A Necessitation A/□A. By adding these and one of the □–◇ biconditionals to a standard axiomatization of classical propositional logic one obtains an axiomatization of the most important modal logic, S5, so named because it is the logic generated by the fifth of the systems in Lewis and Langford’s Symbolic Logic (1932). S5 can be characterized more directly by possible-worlds models. Each such model specifies a set of possible worlds and assigns truth-values to atomic sentences relative to these worlds. Truth-values of classical compounds at a world w depend in the usual way on truth-values of their components. □A is true at w if A is true at all worlds of the model; ◇A, if A is true at some world of the model. S5 comprises the formulas true at all worlds in all such models. Many modal logics weaker than S5 can be characterized by models which specify, besides a set of possible worlds, a relation of ‘accessibility’ or relative possibility on this set. □A is true at a world w if A is true at all worlds accessible from w, that is, at all worlds that would be possible if w were actual. Of the schemas listed above, only K is true in all these models, but each of the others is true when accessibility meets an appropriate constraint. The addition of modal operators to predicate logic poses additional conceptual and mathematical difficulties. On one conception a model for quantified modal logic specifies, besides a set of worlds, the set Dw of individuals that exist in w, for each world w. For example, ∃x□A is true at w if there is some element of Dw that satisfies A in every possible world. If A is satisfied only by existent individuals in any given world ∃x□A thus implies that there are necessary individuals; individuals that exist in every accessible possible world. If A is satisfied by non-existents there can be models and assignments that satisfy A, but not ∃xA. Consequently, on this conception modal predicate logic is not an extension of its classical counterpart. The modern development of modal logic has been criticized on several grounds, and some philosophers have expressed scepticism about the intelligibility of the notion of necessity that it is supposed to describe.

Classical theism and modal realism are incompatible

2016 ◽  
Vol 52 (4) ◽  
pp. 561-572 ◽  
Author(s):  
CHAD VANCE
Keyword(s):  
Actual World ◽  
Possible Worlds ◽  
David Lewis ◽  
Counterpart Theory ◽  
Possible Worlds Semantics ◽  
Intrinsic Properties ◽  
Modal Realism ◽  
Possible World ◽  
Necessary Being ◽  
Special Case

AbstractThe classical conception of God is that of a necessary being. On a possible worlds semantics, this entails that God exists at every possible world. According to the modal realist account of David Lewis, possible worlds are understood to be real, concrete worlds – no different in kind from the actual world. But, modal realism is equipped to accommodate the existence of a necessary being in only one of three ways: (1) By way of counterpart theory, or (2) by way of a special case of trans-world identity for causally inert necessary beings (e.g. pure sets), or else (3) causally potent ones which lack accidental intrinsic properties. I argue that each of these three options entails unacceptable consequences – (1) and (2) are incompatible with theism, and (3) is incompatible with modal realism. I conclude that (at least) one of these views is false.

From “Possible Worlds” to “Possible Experience”. Real Possibility in Leibniz and Kant

Kant Yearbook ◽  
2014 ◽  
Vol 6 (1) ◽  
Author(s):  
Osvaldo Ottaviani
Keyword(s):  
Actual World ◽  
Possible Worlds ◽  
Pure Reason ◽  
Critique Of Pure Reason ◽  
Possible World ◽  
Short Account ◽  
Real Possibility ◽  
The Real ◽  
Conditions Of Possibility ◽  
Metaphysics Of Modality

AbstractThis paper moves from a disagreement with those interpreters who explain Kant’s doctrine of real possibility in terms of possible worlds. It seems to me that a possible world framework is too much indebted to the Leibnizian metaphysics of modality and, therefore, cannot serve to make sense of Kant’s theses. Leibniz’s theory of possibility, indeed, has been deeply criticized in Kant’s Critique of Pure Reason (CPR). Interestingly enough, however, Kant’s principal argument for rejecting that the field of what is possible is greater than the field of what is real was already anticipated by Leibniz. However, Leibniz employed it to demonstrate that there cannot be more than one actual world only (the others being purely possible ones). Moving from this fact, I argue that there is a certain tension between what Leibniz says about the actual world and his commitment to a plurality of possible worlds conceived as ideas in God’s mind. The first part of my paper is devoted to show that such a tension can be traced back to Leibniz’s claims about the relation between the possible and the real. In the second part, then, I maintain that Kant’s theory of real possibility grows from a dissatisfaction with (and a rejection of) Leibniz’s attempted solution to the problem of characterizing a kind of possibility narrower than the merely logical one and, nonetheless, not identical with existence. Finally, I present a short account of Kant’s theory of real possibility, based on the notion of transcendental conditions as conditions of possibility of experience, showing how it works in the case of the forms of intuition.

Taking Possible Worlds Seriously

2019 ◽  
pp. 106-126
Author(s):  
Palle Yourgrau
Keyword(s):  
Modal Logic ◽  
Real World ◽  
Actual World ◽  
Possible Worlds ◽  
David Lewis ◽  
Saul Kripke ◽  
Abstract Entities

The discussion so far has been employing the notion of possible worlds, popularized via the semantics of modal logic. How seriously, however, should possible worlds be taken? David Lewis held them to be genuine, concrete worlds, no less real than ours, the actual world, whereas Robert Stalnaker and Saul Kripke take them to be, rather, abstract entities, properties of the actual world—the only real world—which it might possibly possess. I agree with Lewis that possible worlds are no less real than the actual world, but I also agree with Stalnaker that only our world actually exists. I affirm that merely possible worlds, though they lack existence, possess being. I develop the notion of possible worlds, in which possible individuals exist, but also point to unsolved problems, such as how to account for the contingency of the actuality of the actual world.

The Metaphysics of Meaning: Propositions and Possible Worlds

2010 ◽  
Author(s):  
Scott Soames
Keyword(s):  
Possible Worlds ◽  
Abstract Objects ◽  
Possible World ◽  
Truth Conditions ◽  
Theories Of Truth ◽  
Cognitive States

This chapter examines two crucial aspects of the metaphysics of meaning—propositions and possible world-states. It reviews why propositions—needed as meanings of sentences and objects of the attitudes—can neither be extracted from theories of truth conditions, nor defined in terms of possible world-states, It then explains why they also cannot be the mysterious, inherently representational, abstract objects they have traditionally been taken to be. Instead of explaining the representationality of sentences and cognitive states in terms of their relations to the supposedly prior and independent representationality of propositions, we must explain the representationality of propositions in terms of the representationality of the cognitive states with which they are connected. A new account of is presented along these lines.

Abstract Objects

Philosophy ◽  
2019 ◽  
Author(s):  
Mark Balaguer
Keyword(s):  
Possible Worlds ◽  
Abstract Objects ◽  
Abstract Object ◽  
Mathematical Objects ◽  
Fictional Objects ◽  
Space And Time ◽  
Vast Literature ◽  
Mental Objects ◽  
Existence Question ◽  
Mental Object

An abstract object is a non-physical, non-mental object that exists outside of space and time and is wholly unextended. For example, one might think that numbers are abstract objects; e.g., it is plausible to think that if the number 3 exists, then it is not a physical or mental object, and it does not exist in space and time. Likewise, one might think that properties and relations are abstract objects; e.g., it is plausible to think that if redness exists, over and above the various red balls and red houses and so on, then it is an abstract object—i.e., it is non-physical, non-mental, non-spatiotemporal, and so on. Other kinds of objects that are often taken by philosophers to be abstract objects are propositions, sentence types, possible worlds, logical objects, and fictional objects. The view the that there are abstract objects—known as platonism—is of course extremely controversial. Many philosophers think there are just no such things as abstract objects. Philosophers who endorse this antiplatonist view have to endorse some other view of objects of the above kinds—i.e., numbers, properties, propositions, etc.; in particular, in connection with each of these kinds of objects, they have to say either that these objects are physical or mental objects or that there are just no such things. There is a vast literature on the existence and nature of abstract objects. This article focuses mostly (but not entirely) on the existence question—that is, the question of whether there are any such things as abstract objects. In addition, it focuses to some extent (though, again, not entirely) on the specific version of this question that is concerned with the existence of abstract mathematical objects.

scholarly journals Computing possible worlds in the history of modern astronomy

2016 ◽  
Vol 20 (1) ◽  
pp. 117
Author(s):  
Osvaldo Pessoa Jr. ◽  
Rafaela Gesing ◽  
Mariana Jó de Souza ◽  
Daniel Carlos de Melo Marcílio
Keyword(s):  
Computer Simulations ◽  
Actual World ◽  
Possible Worlds ◽  
Computational Simulations ◽  
Consistency Check ◽  
Possible World ◽  
History Of ◽  
The Mean ◽  
Definition Of ◽  
Modern Astronomy

http://dx.doi.org/10.5007/1808-1711.2016v20n1p117As part of an ongoing study of causal models in the history of science, a counterfactual scenario in the history of modern astronomy is explored with the aid of computer simulations. After the definition of “linking advance”, a possible world involving technological antecedence is described, branching out in 1510, in which the telescope is invented 70 years before its actual construction, at the time in which Fracastoro actually built the first prototelescope. By using the principle of the closest possible world (PCP), we estimate that in this scenario the discovery of the elliptical orbit of Mars would by anticipated by only 28 years. The second part of the paper involves an estimate of the probability of the previous scenario, guided by the principle that the actual world is the mean (PAM) and using computer simulations to create possible worlds in which the time spans between advances is varied according to a gamma distribution function. Taking into account the importance of the use of the diaphragm for the invention of the telescope, the probability that the telescope were built by 1538 for a branching time at 1510 is found to be smaller than 1%. The work shows that one of the important features of computational simulations in philosophy of science is to serve as a consistency check for the intuitions and speculations of the philosopher.

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