Those theorists who use the concept of possible worlds consider the actual world in which we live to be one of the many possible worlds. For each distinct way the world could have been, there is said to be a distinct possible world. Among such theorists there is disagreement about the nature of possible worlds; their precise ontological status is disputed, and especially the difference, if any, in ontological status between the actual world and all the other possible worlds. One position on these matters is set forth in David Lewis's modal realism (see below). There is a close relation between propositions and possible worlds. We note that every proposition is either true or false at any given possible world; then the modal status of a proposition is understood in terms of the worlds in which it is true and worlds in which it is false. The following are among the assertions we may now usefully make:
The idea of possible worlds is most commonly attributed to Gottfried Leibniz, who spoke of possible worlds as ideas in the mind of God and used the notion to argue that our actually created world must be "the best of all possible worlds". Arthur Schopenhauer argued that on the contrary our world must be the worst of all possible worlds, because if it were only a little worse it could not continue to exist.
Scholars have found implicit earlier traces of the idea of possible worlds in the works of René Descartes, a major influence on Leibniz, Al-Ghazali (The Incoherence of the Philosophers), Averroes (The Incoherence of the Incoherence), Fakhr al-Din al-Razi (Matalib al-'Aliya) and John Duns Scotus. The modern philosophical use of the notion was pioneered by David Lewis and Saul Kripke.
A semantics for modal logic was first introduced in the late-1950s work of Saul Kripke and his colleagues. A statement in modal logic that is possible is said to be true in at least one possible world; a statement that is necessary is said to be true in all possible worlds.
From this groundwork, the theory of possible worlds became a central part of many philosophical developments, from the 1960s onwards – including, most famously, the analysis of counterfactual conditionals in terms of "nearby possible worlds" developed by David Lewis and Robert Stalnaker. On this analysis, when we discuss what would happen if some set of conditions were the case, the truth of our claims is determined by what is true at the nearest possible world (or the set of nearest possible worlds) where the conditions obtain. (A possible world W1 is said to be near to another possible world W2 in respect of R to the degree that the same things happen in W1 and W2 in respect of R; the more different something happens in two possible worlds in a certain respect, the "further" they are from one another in that respect.) Consider this conditional sentence: "If George W. Bush hadn't become president of the U.S. in 2001, Al Gore would have." The sentence would be taken to express a claim that could be reformulated as follows: "In all nearest worlds to our actual world (nearest in relevant respects) where George W. Bush didn't become president of the U.S. in 2001, Al Gore became president of the U.S. then instead." And on this interpretation of the sentence, if there is or are some nearest worlds to the actual world (nearest in relevant respects) where George W. Bush didn't become president but Al Gore didn't either, then the claim expressed by this counterfactual would be false.
Today, possible worlds play a central role in many debates in philosophy, including especially debates over the Zombie Argument, and physicalism and supervenience in the philosophy of mind. Many debates in the philosophy of religion have been reawakened by the use of possible worlds. Intense debate has also emerged over the ontological status of possible worlds, provoked especially by David Lewis's defense of modal realism, the doctrine that talk about "possible worlds" is best explained in terms of innumerable, really existing worlds beyond the one we live in. The fundamental question here is: given that modal logic works, and that some possible-worlds semantics for modal logic is correct, what has to be true of the world, and just what are these possible worlds that we range over in our interpretation of modal statements? Lewis argued that what we range over are real, concrete worlds that exist just as unequivocally as our actual world exists, but that are distinguished from the actual world simply by standing in no spatial, temporal, or causal relations with the actual world. (On Lewis's account, the only "special" property that the actual world has is a relational one: that we are in it. This doctrine is called "the indexicality of actuality": "actual" is a merely indexical term, like "now" and "here".) Others, such as Robert Adams and William Lycan, reject Lewis's picture as metaphysically extravagant, and suggest in its place an interpretation of possible worlds as consistent, maximally complete sets of descriptions of or propositions about the world, so that a "possible world" is conceived of as a complete description of a way the world could be – rather than a world that is that way. (Lewis describes their position, and similar positions such as those advocated by Alvin Plantinga and Peter Forrest, as "ersatz modal realism", arguing that such theories try to get the benefits of possible worlds semantics for modal logic "on the cheap", but that they ultimately fail to provide an adequate explanation.) Saul Kripke, in Naming and Necessity, took explicit issue with Lewis's use of possible worlds semantics, and defended a stipulative account of possible worlds as purely formal (logical) entities rather than either really existent worlds or as some set of propositions or descriptions.
Possible worlds theory in literary studies uses concepts from possible-world logic and applies them to worlds that are created by fictional texts, fictional universe. In particular, possible-world theory provides a useful vocabulary and conceptual framework with which to describe such worlds. However, a literary world is a specific type of possible world, quite distinct from the possible worlds in logic. This is because a literary text houses its own system of modality, consisting of actual worlds (actual events) and possible worlds (possible events). In fiction, the principle of simultaneity, it extends to cover the dimensional aspect, when it is contemplated that two or more physical objects, realities, perceptions and objects non-physical, can coexist in the same space-time. Thus, a literary universe is granted autonomy in much the same way as the actual universe.
Literary critics, such as Marie-Laure Ryan, Lubomír Doležel, and Thomas Pavel, have used possible-worlds theory to address notions of literary truth, the nature of fictionality, and the relationship between fictional worlds and reality. Taxonomies of fictional possibilities have also been proposed where the likelihood of a fictional world is assessed. Possible-world theory is also used within narratology to divide a specific text into its constituent worlds, possible and actual. In this approach, the modal structure of the fictional text is analysed in relation to its narrative and thematic concerns. Rein Raud has extended this approach onto "cultural" worlds, comparing possible worlds to the particular constructions of reality of different cultures. However, the metaphor of the "cultural possible worlds" relates to the framework of cultural relativism and, depending on the ontological status ascribed to possible worlds, warrants different, often controversial claims ranging from ethnocentrism to cultural imperialism.
The Latin phrases a priori (lit. "from the earlier") and a posteriori (lit. "from the later") are philosophical terms popularized by Immanuel Kant's Critique of Pure Reason (first published in 1781, second edition in 1787), one of the most influential works in the history of philosophy. However, in their Latin forms they appear in Latin translations of Euclid's Elements, of about 300 BC, a work widely considered during the early European modern period as the model for precise thinking.
These terms are used with respect to reasoning (epistemology) to distinguish "necessary conclusions from first premises" (i.e., what must come before sense observation) from "conclusions based on sense observation" which must follow it. Thus, the two kinds of knowledge, justification, or argument, may be glossed:
A priori knowledge or justification is independent of experience, as with mathematics (3 + 2 = 5), tautologies ("All bachelors are unmarried"), and deduction from pure reason (e.g., ontological proofs).
A posteriori knowledge or justification depends on experience or empirical evidence, as with most aspects of science and personal knowledge.There are many points of view on these two types of knowledge, and their relationship gives rise to one of the oldest problems in modern philosophy.
The terms a priori and a posteriori are primarily used as adjectives to modify the noun "knowledge" (for example, "a priori knowledge"). However, "a priori" is sometimes used to modify other nouns, such as "truth". Philosophers also may use "apriority" and "aprioricity" as nouns to refer (approximately) to the quality of being "a priori".Although definitions and use of the terms have varied in the history of philosophy, they have consistently labeled two separate epistemological notions. See also the related distinctions: deductive/inductive, analytic/synthetic, necessary/contingent.Actualism
In contemporary analytic philosophy, actualism is the view that everything there is (i.e., everything that has being, in the broadest sense) is actual. Another phrasing of the thesis is that the domain of unrestricted quantification ranges over all and only actual existents.The denial of actualism is possibilism, the thesis that there are some entities that are merely possible: these entities have being but are not actual and, hence, enjoy a "less robust" sort of being than do actually existing things. An important, but significantly different notion of possibilism known as modal realism was developed by the philosopher David Lewis. On Lewis's account, the actual world is identified with the physical universe of which we are all a part. Other possible worlds exist in exactly the same sense as the actual world; they are simply spatio-temporally unrelated to our world, and to each other. Hence, for Lewis, "merely possible" entities—entities that exist in other possible worlds—exist in exactly the same sense as do we in the actual world; to be actual, from the perspective of any given individual x in any possible world, is simply to be part of the same world as x.Alvin Plantinga
Alvin Carl Plantinga (; born November 15, 1932) is a prominent American analytic philosopher who works primarily in the fields of logic, justification, philosophy of religion, and epistemology.
From 1963-82, Plantinga taught at Calvin College before accepting an appointment as the John A. O'Brien Professor of Philosophy at the University of Notre Dame. He later returned to Calvin College to become the inaugural holder of the Jellema Chair in Philosophy.A prominent Christian philosopher, Plantinga served as president of the Society of Christian Philosophers from 1983-86. He has delivered the Gifford Lectures two times and was described by TIME magazine as "America's leading orthodox Protestant philosopher of God". William Lane Craig wrote in his work Reasonable Faith that he considers Plantinga to be the greatest Christian philosopher alive. A fellow of the American Academy of Arts and Sciences, he was awarded the Templeton Prize in 2017.Some of Plantinga's most influential works including God and Other Minds (1967), The Nature of Necessity (1974), and a trilogy of books on epistemology, culminating in Warranted Christian Belief (2000) that was simplified in Knowledge and Christian Belief (2016).Counterfactual conditional
A counterfactual conditional (abbreviated CF), is a conditional containing an if-clause which is contrary to fact. The term "counterfactual conditional" was coined by Nelson Goodman in 1947, extending Roderick Chisholm's (1946) notion of a "contrary-to-fact conditional". The study of counterfactual speculation has increasingly engaged the interest of scholars in a wide range of domains such as philosophy, human geography, psychology, cognitive psychology, history, political science, economics, social psychology, law, organizational theory, marketing, and epidemiology.In 1748, when defining causation, David Hume referred to a counterfactual case:
"… we may define a cause to be an object, followed by another, and where all objects, similar to the first, are followed by objects similar to the second. Or in other words, where, if the first object had not been, the second never had existed …" — David Hume, An Enquiry Concerning Human Understanding.
Counterfactualism is the view that dispositions are a type of counterfactual property.Counterpart theory
In philosophy, specifically in the area of modal metaphysics, counterpart theory is an alternative to standard (Kripkean) possible-worlds semantics for interpreting quantified modal logic. Counterpart theory still presupposes possible worlds, but differs in certain important respects from the Kripkean view. The form of the theory most commonly cited was developed by David Lewis, first in a paper and later in his book On the Plurality of Worlds.Cueva Fell
Cueva Fell is a natural cave and archaeological site in southern Patagonia. Cueva Fell is in proximity to the Pali Aike Crater, another significant archaeological site. Cueva Fell combined with the nearby Pali Aike site have been submitted to UNESCO as a possible World Heritage Site.David Lewis (philosopher)
David Kellogg Lewis (September 28, 1941 – October 14, 2001) was an American philosopher. Lewis taught briefly at UCLA and then at Princeton from 1970 until his death. He is also closely associated with Australia, whose philosophical community he visited almost annually for more than thirty years. He made contributions in philosophy of language, philosophy of mind, philosophy of probability, metaphysics, epistemology, philosophical logic, and aesthetics. He is probably best known for his controversial modal realist stance: that (i) possible worlds exist, (ii) every possible world is a concrete entity, (iii) any possible world is causally and spatiotemporally isolated from any other possible world, and (iv) our world is among the possible worlds.Epistemic modal logic
Epistemic modal logic is a subfield of modal logic that is concerned with reasoning about knowledge. While epistemology has a long philosophical tradition dating back to Ancient Greece, epistemic logic is a much more recent development with applications in many fields, including philosophy, theoretical computer science, artificial intelligence, economics and linguistics. While philosophers since Aristotle have discussed modal logic, and Medieval philosophers such as Avicenna, Ockham, and Duns Scotus developed many of their observations, it was C. I. Lewis who created the first symbolic and systematic approach to the topic, in 1912. It continued to mature as a field, reaching its modern form in 1963 with the work of Kripke.Epistemic modality
Epistemic modality is a sub-type of linguistic modality that deals with a speaker's evaluation/judgment of, degree of confidence in, or belief of the knowledge upon which a proposition is based. In other words, epistemic modality refers to the way speakers communicate their doubts, certainties, and guesses—their "modes of knowing". More technically, epistemic modality may be defined "...as (the linguistic expression of) an evaluation of the chances that a certain hypothetical state of affairs under consideration (or some aspect of it) will occur, is occurring, or has occurred in a possible world which serves as the universe of interpretation for the evaluation process… In other words, epistemic modality concerns an estimation of the likelihood that (some aspect of) a certain state of affairs is/has been/will be true (or false) in the context of the possible world under consideration. This estimation of likelihood is situated on a scale going from certainty that the state of affairs applies, via a neutral or agnostic stance towards its occurrence, to certainty that it does not apply, with intermediary positions on the positive and the negative sides of the scale".Being a sub-type of linguistic modality, epistemic modality can in its turn be classified into a number of sub-types according to various criteria. An original classification of epistemic modality based on the conception of alienated knowledge is given in the work of V. A. Yatsko.Irenaean theodicy
The Irenaean theodicy is a Christian theodicy (a response to the problem of evil). It defends the probability of an omnipotent and omnibenevolent (all-powerful and perfectly loving) God in the face of evidence of evil in the world. Numerous variations of theodicy have been proposed which all maintain that, while evil exists, God is either not responsible for creating evil, or he is not guilty for creating evil. Typically, the Irenaean theodicy asserts that the world is the best of all possible worlds because it allows humans to fully develop. Most versions of the Irenaean theodicy propose that creation is incomplete, as humans are not yet fully developed, and experiencing evil and suffering is necessary for such development.
Second-century philosopher and theologian Irenaeus, after whom the theodicy is named, proposed a two-stage creation process in which humans require free will and the experience of evil to develop. Another early Christian theologian, Origen, presented a response to the problem of evil which cast the world as a schoolroom or hospital for the soul; theologian Mark Scott has argued that Origen, rather than Irenaeus, ought to be considered the father of this kind of theodicy. Friedrich Schleiermacher argued in the nineteenth century that God must necessarily create flawlessly, so this world must be the best possible world because it allows God's purposes to be naturally fulfilled. In 1966, philosopher John Hick discussed the similarities of the preceding theodicies, calling them all "Irenaean". He supported the view that creation is incomplete and argued that the world is best placed for the full moral development of humans, as it presents genuine moral choices. British philosopher Richard Swinburne proposed that, to make a free moral choice, humans must have experience of the consequences of their own actions and that natural evil must exist to provide such choices.
The development of process theology has challenged the Irenaean tradition by teaching that God's power is limited and that he cannot be responsible for evil. Twentieth-century philosopher Alvin Plantinga opposed the idea that this is the best possible world, arguing that there could always be at least one more good person, in every possible world. His free will defence was not a theodicy because he was trying to show the logical compatibility of evil and the existence of God, rather than the probability of God. D. Z. Phillips and Fyodor Dostoyevsky challenged the instrumental use of suffering, suggesting that love cannot be expressed through suffering. However, Dostoyevsky also states that the beauty of love is evident, in that love can continue to grow, withstand and overcome even the most evil acts. Michael Tooley argued that the magnitude of suffering is excessive and that, in some cases, cannot lead to moral development. French theologian Henri Blocher criticised Hick's universalism, arguing that such a view negates free will, which was similarly important to the theodicy.Logical consequence
Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically follows from one or more statements. A valid logical argument is one in which the conclusion is entailed by the premises, because the conclusion is the consequence of the premises. The philosophical analysis of logical consequence involves the questions: In what sense does a conclusion follow from its premises? and What does it mean for a conclusion to be a consequence of premises? All of philosophical logic is meant to provide accounts of the nature of logical consequence and the nature of logical truth.
Logical consequence is necessary and formal, by way of examples that explain with formal proof and models of interpretation. A sentence is said to be a logical consequence of a set of sentences, for a given language, if and only if, using only logic (i.e. without regard to any personal interpretations of the sentences) the sentence must be true if every sentence in the set is true.
Logicians make precise accounts of logical consequence regarding a given language , either by constructing a deductive system for or by formal intended semantics for language . The Polish logician Alfred Tarski identified three features of an adequate characterization of entailment: (1) The logical consequence relation relies on the logical form of the sentences, (2) The relation is a priori, i.e. it can be determined with or without regard to empirical evidence (sense experience), and (3) The logical consequence relation has a modal component.Logical truth
Logical truth is one of the most fundamental concepts in logic, and there are different theories on its nature. A logical truth is a statement which is true, and remains true under all reinterpretations of its components other than its logical constants. It is a type of analytic statement. All of philosophical logic can be thought of as providing accounts of the nature of logical truth, as well as logical consequence.Logical truths (including tautologies) are truths which are considered to be necessarily true. This is to say that they are considered to be such that they could not be untrue and no situation could arise which would cause us to reject a logical truth. It must be true in every sense of intuition, practices, and bodies of beliefs. However, it is not universally agreed that there are any statements which are necessarily true.
A logical truth is considered by some philosophers to be a statement which is true in all possible worlds. This is contrasted with facts (which may also be referred to as contingent claims or synthetic claims) which are true in this world, as it has historically unfolded, but which is not true in at least one possible world, as it might have unfolded. The proposition "If p and q, then p" and the proposition "All married people are married" are logical truths because they are true due to their inherent structure and not because of any facts of the world.
Later, with the rise of formal logic a logical truth was considered to be a statement which is true under all possible interpretations.
The existence of logical truths has been put forward by rationalist philosophers as an objection to empiricism because they hold that it is impossible to account for our knowledge of logical truths on empiricist grounds. Empiricists commonly respond to this objection by arguing that logical truths (which they usually deem to be mere tautologies), are analytic and thus do not purport to describe the world.Metaphysical nihilism
Metaphysical nihilism is the philosophical theory that there might have been no objects at all—that is, that there is a possible world in which there are no objects at all; or at least that there might have been no concrete objects at all, so that even if every possible world contains some objects, there is at least one that contains only abstract objects.To understand metaphysical nihilism, one can look to the subtraction theory in its simplest form, proposed by Thomas Baldwin.
There could have been finitely many things.
For each thing, that thing might not have existed.
The removal of one thing does not necessitate the introduction of another.
Therefore, there could have been no things at all.The idea is that there is a possible world with finitely many things. One can thus get another possible world by taking a single thing away, and one does not need to add any other thing as its replacement. Then one can take another thing away, and another, until one is left with a possible world that is empty.
Against the possible strength of this intuitive argument, some philosophers argue that there are necessarily some concrete objects. It is a consequence of David Kellogg Lewis's concrete modal realism that it is impossible that no concrete objects exist; for since worlds are concrete, there is at least one concrete object—the world itself—at each world. E. J. Lowe has likewise argued that there are necessarily some concrete objects. His argument runs as follows: Necessarily, there are some abstract objects, such as numbers. The only possible abstract objects are sets or universals, but both of these depend on the existence of concrete objects (for sets, their members; for universals, the things that instantiate them). Therefore, there are necessarily some concrete objects.Modal logic
Modal logic is a type of formal logic primarily developed in the 1960s that extends classical propositional and predicate logic to include operators expressing modality. A modal—a word that expresses a modality—qualifies a statement. For example, the statement "John is happy" might be qualified by saying that John is usually happy, in which case the term "usually" is functioning as a modal. The traditional alethic modalities, or modalities of truth, include possibility ("Possibly, p", "It is possible that p"), necessity ("Necessarily, p", "It is necessary that p"), and impossibility ("Impossibly, p", "It is impossible that p"). Other modalities that have been formalized in modal logic include temporal modalities, or modalities of time (notably, "It was the case that p", "It has always been that p", "It will be that p", "It will always be that p"), deontic modalities (notably, "It is obligatory that p", and "It is permissible that p"), epistemic modalities, or modalities of knowledge ("It is known that p") and doxastic modalities, or modalities of belief ("It is believed that p").
A formal modal logic represents modalities using modal operators. For example, "It might rain today" and "It is possible that rain will fall today" both contain the notion of possibility. In a modal logic this is represented as an operator, "Possibly", attached to the sentence "It will rain today".
It is fallacious to confuse necessity and possibility. In particular, this is known as the modal fallacy.
The basic unary (1-place) modal operators are usually written "□" for "Necessarily" and "◇" for "Possibly". Following the example above, if is to represent the statement of "it will rain today", the possibility of rain would be represented by . This reads: It is possible that it will rain today. Similarly reads: It is necessary that it will rain today, expressing certainty regarding the statement.
In a classical modal logic, each can be expressed by the other with negation.
In natural language, this reads: it is possible that it will rain today if and only if it is not necessary that it will not rain today. Similarly, necessity can be expressed in terms of possibility in the following negation:
which states it is necessary that it will rain today if and only if it is not possible that it will not rain today. Alternative symbols used for the modal operators are "L" for "Necessarily" and "M" for "Possibly".Modal realism
Modal realism is the view propounded by David Kellogg Lewis that all possible worlds are real in the same way as is the actual world: they are "of a kind with this world of ours." It is based on the following tenets: possible worlds exist; possible worlds are not different in kind from the actual world; possible worlds are irreducible entities; the term actual in actual world is indexical, i.e. any subject can declare their world to be the actual one, much as they
label the place they are "here" and the time they are "now".Ontological argument
An ontological argument is a philosophical argument for the existence of God that uses ontology. Many arguments fall under the category of the ontological, and they tend to involve arguments about the state of being or existing. More specifically, ontological arguments tend to start with a priori theory about the organization of the universe. If that organizational structure is true, the argument will provide reasons why God must exist.
The first ontological argument in the [Western Christian] tradition was proposed by Anselm of Canterbury in his 1078 work Proslogion. Anselm defined God as "that than which nothing greater can be thought", and argued that this being must exist in the mind, even in the mind of the person who denies the existence of God. He suggested that, if the greatest possible being exists in the mind, it must also exist in reality. If it exists only in the mind, then an even greater being must be possible—one which exists both in the mind and in reality. Therefore, this greatest possible being must exist in reality. Seventeenth-century French philosopher René Descartes deployed a similar argument. Descartes published several variations of his argument, each of which centred on the idea that God's existence is immediately inferable from a "clear and distinct" idea of a supremely perfect being. In the early eighteenth century, Gottfried Leibniz augmented Descartes' ideas in an attempt to prove that a "supremely perfect" being is a coherent concept. A more recent ontological argument came from Kurt Gödel, who proposed a formal argument for God's existence. Norman Malcolm revived the ontological argument in 1960 when he located a second, stronger ontological argument in Anselm's work; Alvin Plantinga challenged this argument and proposed an alternative, based on modal logic. Attempts have also been made to validate Anselm's proof using an automated theorem prover. Other arguments have been categorised as ontological, including those made by Islamic philosophers Mulla Sadra and Allama Tabatabai.
Since its proposal, few philosophical ideas have generated as much interest and discussion as the ontological argument. Nearly all of the great minds of Western philosophy have found the argument worthy of their attention, and a number of criticisms and objections have been mounted. The first critic of the ontological argument was Anselm's contemporary, Gaunilo of Marmoutiers. He used the analogy of a perfect island, suggesting that the ontological argument could be used to prove the existence of anything. This was the first of many parodies, all of which attempted to show that the argument has absurd consequences. Later, Thomas Aquinas rejected the argument on the basis that humans cannot know God's nature. Also, David Hume offered an empirical objection, criticising its lack of evidential reasoning and rejecting the idea that anything can exist necessarily. Immanuel Kant's critique was based on what he saw as the false premise that existence is a predicate. He argued that "existing" adds nothing (including perfection) to the essence of a being, and thus a "supremely perfect" being can be conceived not to exist. Finally, philosophers including C. D. Broad dismissed the coherence of a maximally great being, proposing that some attributes of greatness are incompatible with others, rendering "maximally great being" incoherent.
Contemporary defenders of the ontological argument include Alvin Plantinga, William Alston and David Bentley Hart.Physicalism
In philosophy, physicalism is the metaphysical thesis that "everything is physical", that there is "nothing over and above" the physical, or that everything supervenes on the physical. Physicalism is a form of ontological monism—a "one substance" view of the nature of reality as opposed to a "two-substance" (dualism) or "many-substance" (pluralism) view. Both the definition of "physical" and the meaning of physicalism have been debated.
Physicalism is closely related to materialism. Physicalism grew out of materialism with advancements of the physical sciences in explaining observed phenomena. The terms are often used interchangeably, although they are sometimes distinguished, for example on the basis of physics describing more than just matter (including energy and physical law). Common arguments against physicalism include both the philosophical zombie argument and the multiple observers argument, that the existence of a physical being may imply zero or more distinct conscious entities.Rigid designator
In modal logic and the philosophy of language, a term is said to be a rigid designator or absolute substantial term when it designates (picks out, denotes, refers to) the same thing in all possible worlds in which that thing exists and does not designate anything else in those possible worlds in which that thing does not exist. A designator is persistently rigid if it designates the same thing in every possible world in which that thing exists and designates nothing in all other possible worlds. A designator is obstinately rigid if it designates the same thing in every possible world, period, whether or not that thing exists in that world. Rigid designators are contrasted with connotative terms, non-rigid or flaccid designators, which may designate different things in different possible worlds.Sense and reference
In the philosophy of language, the distinction between sense and reference was an innovation of the German philosopher and mathematician Gottlob Frege in 1892 (in his paper "On Sense and Reference"; German: "Über Sinn und Bedeutung"), reflecting the two ways he believed a singular term may have meaning.
The reference (or "referent"; Bedeutung) of a proper name is the object it means or indicates (bedeuten), its sense (Sinn) is what the name expresses. The reference of a sentence is its truth value, its sense is the thought that it expresses. Frege justified the distinction in a number of ways.
Sense is something possessed by a name, whether or not it has a reference. For example, the name "Odysseus" is intelligible, and therefore has a sense, even though there is no individual object (its reference) to which the name corresponds.
The sense of different names is different, even when their reference is the same. Frege argued that if an identity statement such as "Hesperus is the same planet as Phosphorus" is to be informative, the proper names flanking the identity sign must have a different meaning or sense. But clearly, if the statement is true, they must have the same reference. The sense is a 'mode of presentation', which serves to illuminate only a single aspect of the referent.Much of analytic philosophy is traceable to Frege's philosophy of language. Frege's views on logic (i.e., his idea that some parts of speech are complete by themselves, and are analogous to the arguments of a mathematical function) led to his views on a theory of reference.