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Unfortunately, our editorial approach may not be able to accommodate all contributions. Our editors will review what you've submitted, and if it meets our criteria, we'll add it to the article. Please note that our editors may make some formatting changes or correct spelling or grammatical errors, and may also contact you if any clarifications are needed. Possible world logic and philosophy. The Editors of Encyclopaedia Britannica. Learn More in these related Britannica articles: Perhaps unicorn is meaningful because of what it would apply to in certain circumstances, though in actuality it does not apply to anything.

And perhaps the descriptions the first president of the United States and the husband of Martha Washington are not synonymous…. The simplest such definition is this: In each world, independently of all the others, let each propositional variable then be assigned either…. On the basis of this observation and certain broader developments in logic, Carnap tried to develop formal treatments of…. Possible-world semantics criterion of logical truth In metalogic: Semiotic modal realism In realism: Ultimately, all genuine possibilities, simple or not, are just states of affairs that exist in these combinatorial worlds in the sense of AE3.

Likewise, it is not entirely clear how combinatorialism accounts for intuitive facts about essential properties, such as that our water molecule W is essentially water or that Algol is essentially a dog. Combinatorialists argue that such modal facts can nevertheless be explained in terms that require no appeal to primitive modal features of the world Armstrong b, Armstrong argues that many intuitive modal facts — notably, the impossibility of an object exemplifying more than one determinate of the same determinable — can be understood ultimately as logical, or analytic, modalities that are grounded in meaning rather than any primitive modal features of reality.

For example, intuitively it is impossible that an object simultaneously exemplify the structural properties having 2kg mass and having 1kg mass. The combinatorial reason for this cf. Armstrong , 79 is that, for an object a to exemplify the former property is simply for there to be a division of a into two wholly distinct parts, both of which exemplify the latter property. Moreover, this division into parts is entirely arbitrary, that is, for any part a 1 of a exemplifying having 1kg mass , there is a unique part a 2 of a wholly distinct from a 1 that also exemplifies that property.

It follows that, if our 2kg object a itself also exemplifies having 1kg mass , then, as a is a part of itself, there must be a 1kg part of a that is wholly distinct from a. Let us suppose the actual world w 1 includes our water molecule W from Figure 1 plus a further hydrogen atom h 3. In this world, only h 1 and h 2 bind to o. Hence, this world includes the state of affairs W's being water but not the state of affairs I's being hydronium in which o , h 1 , h 2 , and h 3 are so bonded as to constitute a hydronium ion I.

Conversely, however, given the unrestricted nature of recombination, there is a world w 2 that includes W structured as it actually is in w 1 but which also includes the spoiler [ B , o , h 3 ] — where o and h 3 bond — and, hence, the structural state of affairs I's being hydronium.

Thus, the absence of [ B , o , h 3 ] in w 1 enables the emergence of W's being water and precludes I's being hydronium whilst its presence in w 2 enables the emergence of the latter but precludes the former. As a consequence, it is impossible that the states of affairs W's being water and I's being hydronium coexist.

W 's being water and given a bond between o and h 3 I 's being hydronium. Although more dramatic, large-scale examples of incompatible states of affairs — such as a thing's being simultaneously both a baboon and a hoolock — might be vastly more complex, there is no obvious reason why their impossibility could not have the same sort of combinatorial explanation.

It follows from the unrestricted nature of recombination that, for any simple object a and simple universal P , a recombines with P in some worlds and fails to recombine with P in others. Generalizing from this fact, it follows that no simple or sum of simples has any simple universal or conjunction of simple universals essentially. It also follows that no such object has any structural property essentially. For assume o is such an object and that it exemplifies a structural property P.

Since P is structural, it supervenes on some set of simple states of affairs. But by the nature of recombination, there are combinatorial worlds in which those states of affairs do not exist and, hence, in which P doesn't but o — being a simple or a sum of simples — does. Thick particulars like our water molecule W don't fare much better because of the possibility of spoilers. For Armstrong , 35 , W is simply the conjunction of its constituent states of affairs. As we've just seen, however, in the presence of spoilers, that conjunction would exist — hence, W would exist — without being Water.

Hence, it would seem that at least some properties that, intuitively, are essential to their bearers turn out not to be for the combinatorialist. The problem is compounded by the fact that some intuitively non-essential properties of some thick particulars are arguably essential for the combinatorialist. The shape properties of a thick particular A , for example, would seem to be a function of its constituent states of affairs. Moreover, the exemplification of such properties are not obviously subject to spoilers the way that natural kind properties like Water are.

Hence, as A is identical to the conjunction of its constituent states of affairs, it would seem that it will have the same shape in any world in which it exists, i. That said, combinatorialism can arguably provide a reasonably robust analysis of intuitions about the essential properties of ordinary thick particulars like dogs or persons. Such objects can be taken to be temporal successions of sums of simples and each sum in the succession as its temporal parts. Sums in the same rough temporal neighborhood are composed of roughly the same simples and are structured in roughly the same way.

Similarities between such objects across worlds in turn determine counterpart relations. Following Lewis, the essential properties of such objects can then be identified with those properties exemplified by all of the temporal parts of all of its counterparts in every world in which it exists Armstrong , 99—, Since a possible world is a recombination of the actual world and every recombination includes states of affairs involving every simple individual and every simple universal, by AE3 , every simple entity exists in every world.

Hence, there could not have been fewer of them; nor could there have been simples other than the ones there actually are. In this section, we address this issue and the issue of contingent existence generally in combinatorialism. Combinatorialism as it stands has no problem accounting for the general intuition that there could have been fewer things. More generally, given the unrestricted nature of recombination, for any a involving a structural fact S , there are recombinations of the actual world wherein either a some of the relations among a 's constituents that are critical to S 's structure fail to be exemplified by those constituents, or b there are further states of affairs included by those recombinations that act as spoilers for S.

Consequently, the combinatorialist seems to have no difficulty explaining how there might have been fewer water molecules, humans, etc. Intuitively, however, there isn't anything in the idea of a simple that suggests that simples are necessary beings — especially if, as combinatorialists generally agree, simples are physical things of some sort and simple universals are properties of, and relations among, those things. For there is nothing in the nature of a simple object to suggest that any given simple had to have existed.

Likewise, there is nothing in the nature of a simple universal to suggest it had to have been exemplified and, hence, on the combinatorialist's own conception of universals, that it had to exist. Otherwise put, as simples exist only insofar as they are constituents of facts, there seems no reason why there couldn't have been a very small number of facts, indeed, just a single simple, atomic, monadic fact and, hence, a lone simple object and a lone simple universal.

Possible world

In fact, however, AW3 can be easily modified to accomodate these intuitions without doing any serious violence to combinatorialist intuitions. AE3 requires no modification, as it was defined with sufficient generality above. Intuitively, not only could there have been fewer things, there could have been more things or, more generally, things other than those that actually exist. As above, combinatorialism as it stands seems able to account for many instances of this intuition: Figure 2 illustrates how a non-actual hydronium ion I might exist in another world.

Likewise, there seems no reason to deny, e. It is not implausible to think that such recombinations can give rise to, say, exotic biological kinds that have no actual instances Armstrong , 55— However, it is far from clear that such possibilities exhaust the modal intuition that other things could have existed. Notably, intuitively, there could have been different simple universals distinct from any that actually exist — different fundamental properties of simples, for example.

Likewise for simple objects. Either way, there seems to be nothing in the idea of a simple object or simple universal that suggests there couldn't have been simples other than, or in addition to, the simples there are in fact. Nor is there any obvious way of modifying the principle to accomodate the intuition in question. The combinatorialist could of course abandon actualism and include merely possible simples into her ontology.

Again, she could follow the new actualists and draw a division between actually concrete and non-actual, possibly concrete simples; or she could introduce Plantinga-style haecceities to go proxy for merely possible simples. But all of these options would be badly out of step with the strong, naturalist motivations for combinatorialism: There is but the one physical world comprising all of the facts; recombinations of at least some of those facts — arbitrary rearrangements of their simple objects and universals — determine the possible worlds.

Mere possibilia , merely possible non- concretia , and non-qualitative haecceities have no real place in that picture. Finally, Sider , suggests that combinatorialists who like Armstrong are modal fictionalists can deal with the problem of missing entities simply by appealing to yet more fictionalism: As the combinatorialist fiction already includes non-actual states of affairs with actually existing constituents, there seems no reason not to extend the fiction to include non-actual states of affairs whose constituents include non-actual particulars and universals.

Fictionalism itself, however, leaves the combinatorialist with the deep problems detailed by Kim , Lycan , and Rosen As with concretism and abstractionism, combinatorialism provides reasonably clear definitions of possible worlds and existence in a world and is noteworthy for its attempt to avoid what might be thought of as the metaphysical excesses of the two competing views. In contrast to concretism, combinatorialism is staunchly actualist: Likewise, in contrast to abstractionism's rather rich and unrestrained ontology of SOAs, combinatorialism's states of affairs are comparatively modest.

Moreover, in contrast to nearly all versions of abstractionism, combinatorialism shares with concretism the virtue of a reductive theory of modality: Modal statements, ultimately, are true or false in virtue of how things stand with respect to worlds that are themselves defined in non-modal terms. Combinatorialism's ontological modesty, however, is also a weakness. For, unlike, the two competing approaches, there are modal intuitions that the combinatorialist is not easily able to account for, notably, the intuition that there could have been other things.

Additional difficulties are discussed in the supplemental document Further Problems for Combinatorialism. The author wishes to express his deep gratitude to Phillip Bricker and Max Cresswell for extensive comments on several drafts of this entry and for numerous illuminating discussions of its content and related topics.

Lizzy Dingemans

The entry is vastly better for their generous input. Errors and other infelicities that remain are of course the sole responsibility of the author. A great deal of this entry was written with the support of the Alexander von Humboldt Foundation while the author was a Visiting Fellow at the Munich Center for Mathematical Philosophy in — Thanks are due to the Center's director, Professor Hannes Leitgeb, for making the author's stay at this remarkable venue possible. Finally, the author would like to express his thanks to the SEP Editors for their extraordinary patience in dealing with the very tardy author of a badly-needed entry.


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Possible Worlds and Modal Logic 1. Three Philosophical Conceptions of Possible Worlds 2. So suppose that John's only pets are two dogs, Algol and BASIC, say, and consider two simple sentences and their formalizations the predicates in question indicating the obvious English counterparts: All John's dogs are mammals: All John's pets are mammals: Hence, in accordance with the classical substitutivity principle for sentences, we can replace the occurrence of 1 with 2 in the false sentence Not all John's dogs are mammals: However, when we make the same substitution in the true sentence Necessarily, all John's dogs are mammals: Specifically, in possible world semantics , the modal operators are interpreted as quantifiers over possible worlds, as expressed informally in the following two general principles: And to these, of course, is added the critical modal case that explicitly interprets the modal operator to be a quantifier over worlds, as we'd initially anticipated informally in our principle Nec: Note that interpreting modal operators as quantifiers over possible worlds provides a nice theoretical justification for the usual definition of the possibility operator in terms of necessity, specifically: For, unpacking the right side of definition 10 according to the negation and necessitation clauses above and invoking the definitions of truth and truth at a world simpliciter , we have: Possibly, one of John's pets is not a mammal: A proposition is any function from worlds to truth values.

A property is any function from worlds to sets of individuals. Algol is a dog essentially: Modal sentences that do not, like Necessarily, all dogs are mammals: Three Philosophical Conceptions of Possible Worlds The power and appeal of basic possible world semantics is undeniable. Two arise with particular force: QW What, exactly, is a possible world? QE What is it for something to exist in a possible world? As he rather poetically expresses it , 1: The world we live in is a very inclusive thing There is nothing so far away from us as not to be part of our world.

Anything at any distance is to be included. Likewise the world is inclusive in time. No long-gone ancient Romans, no long-gone pterodactyls, no long-gone primordial clouds of plasma are too far in the past, nor are the dead dark stars too far in the future, to be part of this same world There are countless other worlds, other very inclusive things.

Our world consists of us and all our surroundings, however, remote in time and space; just as it is one big thing having lesser things as parts, so likewise do other worlds have lesser other-worldly things as parts. Then we have the following concretist answers to our questions: Nonetheless, it is useful to express the logical forms of these truth conditions explicitly in terms of worlds, existence in a world in the sense of AE1 , of course , and the counterpart relation, which will be discussed shortly: For every world w , every individual x in w that is a dog is a mammal: For example, since Algol is in fact a pet, given worldboundedness and the definition AE1 of existence in a world w , we have: There is no world w such that Algol exists in w and fails to be someone's pet: Thus, when we analyze 16 accordingly, we have the entirely unproblematic concretist truth condition: Algol is a pet, but there is a world in which exists a counterpart of hers that is not: A proposition is any set of worlds.

A property is any set of individuals. Toward this end, Lewis initially considers the evocative principle: Ways Absolutely every way that a world could be is a way that some world is. Given that individuals are worldbound, however, the principle is expressed more rigorously and more generally in terms of other-worldly duplicates: R1 For any finite or infinite number of objects a 1 , a 2 , R2 For any world w any finite or infinite number of objects a 1 , a 2 , Thus, for example, that things could be in the simple state described above might be spelled out in one of the following ways: The proposition that Anne is in her office and at her desk is possibly true.

Abstractionist possible worlds are now definable straightaway: Accordingly, the abstractionist defines existence in a world simply to be a special case of the inclusion relation: There is a possible world w and an individual a in w such that a is an Exotic in w , which, a bit less formally, is simply to say that Some individual is an Exotic in some possible world.

There is a possible world w and an individual a that is i concrete in w and ii an Exotic in w. So reinterpreted, the truth condition for 23 is: There is a possible world w and a haecceity h that is i exemplified in w and ii coexemplified with the property being an Exotic in w. More generally, atomic facts exist according to the following principle: AF Objects a 1 , Nominalism and Realism , Cambridge: A Theory of Universals , Cambridge: La Structure du Mond: Truth and Truthmakers , Cambridge: Translated in Cresswell forthcoming.

Oxford University Press, — The University of Chicago Press. The Worlds of Possibility , Oxford: Clarendon Press Copeland, B. Reprinted in Loux , — Logics and Languages , London, Methuen. PossibleWorlds and Their Rivals. Dordrecht, Kluwer Academic Publishers. Language in the World. Themes in Philosophical Logic , London: Routledge and Kegan Paul. Possible Worlds , London: The Metaphysics of Modality , Oxford: Modal Logic for Philosophers. Logic and the Modalities in the Twentieth Century.

An Introduction to Modal Logic , London: Provability in Logic , Stockholm: Cambridge University Press, 41— Counterfactuals , Cambridge, Massachussetts: On The Plurality of Worlds , Oxford: Parts of Classes , Oxford: Symbolic Logic , New York: The Possible and the Actual , Ithaca: Essays in Honour of D. Cambridge University Press, 3— North-Holland Publishing Company, —29; reprinted in H.

University of Notre Dame Press , — Essays on the Legacy of Arthur Prior , Oxford: Metaphysics and Truthmakers , Frankfurt am Main: Yale University Press Moreland, J. The Nature of Necessity , Oxford: Worlds, Times, and Selves , Amherst: University of Massachusetts Press. Word and Object , Cambridge, MA: Revista Hispanoamericana de Filosofia , 2 5: Reprinted in Russell , — and published in book form as Russell Logic and Knowledge , London: The Philosophy of Logical Atomism , with an introduction by D.

Metaphysical Foundations of Modal Semantics , Princeton: Logic, Semantics, Metamathematics, papers from to , edited by John Corcoran.

The Possible World by Liese O'Halloran Schwarz

Alvin Plantinga , Dordrecht: University of Minnesota Press, — Modal Logic as Metaphysics. Tractatus Logico-Philosophicus , trans. Ben doesn't speak when the police, and Lucy herself try to talk to him to see how he is feelin Review can be found on my blog here: Ben doesn't speak when the police, and Lucy herself try to talk to him to see how he is feeling and to get some answers about that fateful and terrifying night.

Without Ben talking they are unable to get any answers at all and are left with nothing but question marks about that night. But how can they get Ben to talk? Does he remember what happened? On the other side of town lives a woman named Clare who will soon be celebrating her th birthday. She has kept many secrets from her past for all of these years and didn't think they mattered anymore. That is until one day she realizes she has to tell her secrets.

The question is, what brings all 3 of the main characters together? They were destined to meet, but why?

This book was a fantastic read from the first chapters through to the end. There were many shocking twists and turns that I did not see coming and many surprises to keep your interest throughout. And who doesn't love a good twisty, turny murder mystery? This book will pull at your heart strings and make you feel many different emotions. I loved how the book was written, how you get a glimpse into each character and their lives, and get an understanding of how they all come together in the end.

Such a compelling, heart warming story that you simply cannot put down. A must read to add to your collection. Feb 12, Patty rated it it was amazing Shelves: The rating and review are my own thoughts and opinions, and have not been influenced by receiving this book to read. The Possible World is a story narrated from 3 points of view.

Each storyline is beautifully executed, and expertly interwoven. We learn about her young life just before the Great Depression, and the path she chose was not an easy one, but it was hers alone and she owned it. Lucy is an extremely competent ER doctor managing the clinical environment, but is adrift when it comes taking control of her personal life. Her husband is the type you just cannot like even though she wants it to work out. The transitions between the POVs are very well done. Time spent reading this book is very satisfying.

Jul 11, Alecia rated it really liked it. I am rounding up a 3. The problem I had was in the to me slightly creaking structure of this book. Told from many points of view, it got a bit confusing to me when it toggled between Ben and Leo, and it took awhile to adjust to time and place differences. The beginning scene is both horrific and told very well. I also thought that the medical scenes with Lucy, the ER Dr. The chapters on Lucy, Be I am rounding up a 3. The chapters on Lucy, Ben, Leo and Clare link them all together.

At first they seem like disparate, isolated stories, but the author makes the connection, and the reader sees it coming about half way through the book. It's a leap of faith, but a sweet one. Most of the main characters are layered and deeply nuanced. I enjoyed the prose and the book's intention, and would read this author again. Feb 19, Sue Fernandez rated it it was amazing.

Thank you to NetGalley and Scribner for an E-arc of this title in exchange for my honest review. I stayed up reading this book long into the night, knowing it would be worth being tired the next day. I love an alternating narration, and The Possible World tells the story from 3 points of view, one of whom is a young child. This seems like it would be difficult to do well, but Schwartz has done just that. A young boy survives a terrible crime, and his story soon gets woven with the past, wit Thank you to NetGalley and Scribner for an E-arc of this title in exchange for my honest review.

A young boy survives a terrible crime, and his story soon gets woven with the past, with a friend of his mom's, and with their back stories. I don't want to give any spoilers, I will say this story eloquently and beautifully weaves the stories together for such an interesting book. This is a book that was bittersweet for me I wanted to finish it, yet I wish I could have savored it even more.

This one is highly recommended. Mar 28, Ann rated it it was amazing. What a stunning story. Three people who have never met but whose lives are affected by each other's actions. This book deals with second chances and a persuasive argument for reincarnation or past lives. Clare is almost years old and living a lonely life in a nursing home. One of the residents makes it her mission to become friends and throughout the book Clare tells Gloria her life's story.

Lucy is an ER doctor who treats Ben, a young boy who survives a massacre. Ben wakes up in the ER beli What a stunning story. Ben wakes up in the ER believing his name is Leo and is searching for a woman named Clare who once took care of him. I couldn't put this book down. This is an author I'll be watching for, she creates very believable characters and writes with compassion and forward thinking. You'll want to have this on your "Keeper" shelf. Jul 27, Lynne White rated it it was amazing. I absolutely loved this book! I wish I could give it more than 5 stars!

I read the last pages in a day. I couldn't get enough of this story of Lucy, Ben, and Clare. Three strangers who meet entirely by chance. Lucy, an ER doctor who treats the young Ben after he witnesses a brutal murder. Clare, the almost year old woman who weaves herself into this heartfelt story. Cliffhanger a few chapters toward the end, but it wraps itself up into an amazing tale of ordinary people who are brought t I absolutely loved this book! Cliffhanger a few chapters toward the end, but it wraps itself up into an amazing tale of ordinary people who are brought together. I really and truly enjoyed this read.

I recommend to all who love a great, character-driven story. This author is a great storyteller but for me the structure of this novel felt contrived and distracted from her main achievements, Clare and Leo - strong, credible characters I came to care for. Some lovely writing here, too. I finished this late last night, then felt bereft. Tempted to go back to the beginning and read it again I loved it that much. Jul 12, Susu added it Shelves: This review has been hidden because it contains spoilers.


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  4. To view it, click here. Apr 11, Sue Bottino rated it it was amazing. One of the best books I've read in a long time. The characters were so rich and so well-developed. This was another read on The Pigeonhole, in fact it's my sixth read with them this year! For those of you who don't know it's like an online book club, reading along with other readers on the web. The book was split into 10 parts, called staves, emailed to me each day.

    I was able to leave comments throughout and interact with the others. This was a beautifully written book tha This was another read on The Pigeonhole, in fact it's my sixth read with them this year! This was a beautifully written book that got under my skin in such a subtle way that I didn't realise until the closing sentences.

    Clare and Ben's stories were definitely my favourite part of the book, especially as Clare was recounting her life to Gloria. Lucy's story was really interesting, although some of the medical descriptions were a bit too much for me at times. I think if you enjoy medical stories you'd enjoy this part. I loved the way the author captivated me with her writing, bringing Clare, Ben and Lucy's so vividly too life and how she seamlessly brought those strands together at the end. Another wonderful read from The Pigeonhole and a book that I thoroughly recommend.

    Mar 10, Jacqueline rated it it was amazing. Thank you Netgalley and publishers for providing an ARC of this title in exchange for an honest opinion. What a wonderful novel The Possible World is! This story unfolds through the perspectives of three narrators: All three harbor pain and darkness in their lives and their stories come together in the most satisfying way. This novel is beautifully written May 29, Judy Collins rated it it was amazing Shelves: The cover of the book caught my eye and the story ended being amazing. It was beautifully written.

    This is one of those books that I find myself randomly thinking about, especially while driving home from work. The characters and their story just stuck with me. I loved everything about it- the story, characters and writing style. The characters just all came together, they ended up being connected even though Ben, Lucy and Clare didn't initially know each other.

    Lucy is an ER doctor. She meets Ben when when he is brought into the ER covered in blood. He was the lone survivor of a horrific birthday party massacre. He tells the doctors his name is Leo and wants to find Clare. Under hypnosis, Ben tells Leo's story.

    Clare is living in a nursing home and is believed to be years old. She ends up making friends with another resident, Gloria. She eventually tells Gloria her story. I may have cried a few times, definitely at the end. I fell in love with the characters especially Clare. Her story was heartbreaking. I feel like I got to know the characters. Even when the book ended I wanted to keep reading about their lives.

    Leo's mom was unbelievable. She didn't seem to have any emotion when she received the telegram, unlike Clare. Clare loved and took care of Leo just like Lucy will for Ben. I definitely recommend this book and look forward to reading more by the author. It was one of my favorite books that I read this year!!! The book follows three people — Ben is a young boy and a survivor of a horrific attack that took his mother and friends. Lucy is a doctor in the midst of a painful break up and an immensely pressured time at work.

    Finally, Clare is a lady living in a care home, not speaking to many people, and refusing to divulge anything about her past, her family, or any aspect of her life, until she meets a friend who persuades her to tell her story. Ultimately, the three stories meet in a way that was completely unexpected. Each thread felt detailed and exciting enough to keep me hooked, and every time the book hinted at how the stories might meet, it spurred me on even more. There are no discussion topics on this book yet. About Liese O'Halloran Schwarz.

    She went to Harvard and then attended medical school at University of Virginia. She specialized in emergency medicine and like most doctors, she can thoroughly ruin dinner parties with tales of Liese O'Halloran Schwarz grew up in Washington, DC after an early childhood overseas.