I worked more on the Comprehensible Philosophy Dictionary (a work in progress). What follows are several new definitions that will be added to it. Let me know if anything should be improved.

**abstractism** – The view that something is *necessary* insofar as it’s true of every consistent set of statements, and something is *possible* insofar as it’s true in at least one consistent set of statements. It’s necessary that oxygen is O_{2} insofar as it’s true that oxygen is O_{2} in every consistent set of statements, and it’s possible for a person to jump over a small rock insofar as at least one consistent set of statements has a person jump over a small rock. Abstractism could be considered to advocate the existence of “abstract entities” insofar as the existence of a consistent set of statements could be considered to be factual for that reason.

**accessible world** – A world that is relevant to our world when we want to determine if something is necessary or possible. For example, we could say that something is necessary if it’s true of all accessible worlds. Perhaps it’s necessary that contradictions are impossible because it’s true of all accessible worlds. An accessible world is not necessarily a world we can actually go to. They could exist outside our universe or only exist conceptually. See “possible world,” “truth conditions,” and “modality” for more information.

**accessibility** – (1) The relevant domain used to determine if something is necessary or possible. It is thought that something is necessary if it “has to be true” for all of the relevant domain, and something is possible if it is true of at least one thing within the relevant domain. For example, some philosophers believe that it’s possible for people to exist because they exist in at least one possible world—the one we live in. See “accessible world,” “possible world,” “truth conditions,” and “modality” for more information. (2) In ordinary language, “accessibility” refers to the ability to have contact with something. For example, people in jail have access to food and water; and citizens of the United States have access to move to any city found in the United States.

**algorithm** – A step-by-step procedure.

**analogical reasoning** – Reasoning using analogies that can be explicitly described as an “argument from analogy.”

**argument** – In mathematics and predicate logic, the term ‘argument’ is sometimes used as a synonym for “operands.”

**argument place** – (1) In logic, it is the number of things that is predicated by a statement. For example, “Gxy” is a statement with two predicated things, so it has two argument places. (In this case “G” can stand for “attacks.” In that case “Gxy” would mean “x attacks y.”) (2) In mathematics, it’s the number of things that are involved with an operation. For example, addition is an operation with two argument places. “2 + 3” has two arguments: “2” and “3.”

**arity** – (1) In logic, it refers to the number of things that are predicated. The statement “Fx” has an arity of one because there’s only one thing being predicated. For example, “F” can stand for “is tall” and in that case “Fx” means “x is tall.” The statement “Gxy” has an arity of two because there’s two things being predicated. For example, “G” could stand for “loves” and in that case “Gxy” means “x loves y.” (2) In mathematics, arity refers to the number of things that are part of an operation. For example, addition requires two numbers. “1+2” is an operation with the following two variables: “1” and “2.”

**argument diagram** – A visual representation of an argument that makes it clear how premises are used to support a conclusion. Argument diagrams generally have numbers written in circles, and each number is used to represent a statement. Consider the following argument—“(i) Socrates is a human. (ii) All humans are mammals. (iii) All mammals are mortal. (iv) Therefore, Socrates is mortal.” An example of an argument diagram that can be used to represent this argument is the following:

**argument map** – A visual representation of an argument that makes it clear how premises are used to support a conclusion. Argument maps are a type of argument diagram, but the premises and conclusions are usually written in boxes. An example of an argument map is the following:

**case-based reasoning** – Reasoning involving the consideration of similar situations or things. For example, a doctor could consider the symptoms and cause of illness of various patients that were observed in the past in order to decide what is likely the cause of an illness of another patient who has certain symptoms. Case-based reasoning uses the following four steps for computer models: (a) Retrieve – consider similar cases. (b) Reuse – predict how the similar cases relate to the current case. (c) Revise – check to see if the similar cases relate to the current case as was predicted and make a new prediction if necessary. (d) Retain – once a prediction seems to be successful, continue to rely on that prediction until revision is necessary. Case-based reasoning is similar to “analogical reasoning.”

**completeness** – See “semantic completeness,” “syntactic completeness” or “expressive completeness.”

**concretism** – The view that possible worlds exist similar to the actual world, and that people from a possible world consider their own world the “actual world.” Concretism is an attempt to explain what it means to say that something is necessary or possible—something is necessary insofar as it’s true in every possible world, and something is possible insofar as it is true in at least one possible world. It is necessary that oxygen is O_{2} insofar as it’s true that oxygen is O_{2} in every possible world, and it’s possible that a person can jump over a small rock insofar as it’s true in at least one possible world. “Concretism” can be contrasted with “abstractism.” See “modality” and “modal realism” for more information.

**consistent logical system** – A logical system with axioms and rules of inference that can’t possibly be used to prove contradictory statements from true premises.

**constant** – (1) See “logical constant” or “predicate constant” for more information. (2) In ordinary language, “constant” refers to staying the same.

**critical reasoning** – A synonym for “critical thinking.”

**decidability** – A question is decidable if we can determine the answer. For example, logical systems are supposed to be able to determine if arguments are valid. An argument that can’t be determined to be valid by a logical system would be “undecidable” by that logical system. Any logical system that can’t determine if an argument is valid is semantically incomplete. See “semantic completeness” for more information.

**deductively complete** – See “syntactic completeness.”

**derivation** – A formal proof of a proposition expressed in formal logic. A derivation can be described as a series of statements that are implied by rules of inference, axioms of a logical system, or other statements that have been derived by those two things. For example, a logical system could have an axiom that states “*a* or not-*a*” and have a rule of inference that states “*a* implies *a* or *b*.” In that case the following is a derivation—“*a* or not-*a. *Therefore, *a* or not-*a* or *b*.” See “axioms,” “rules of inference,” “logical system,” and “theorem” for more information.

**epistemic vigilance** – Attributes and mechanisms that help people avoid deception, manipulation, and confusion. For example, we intuitively tend not to trust claims that seem to be “too good to be true” from people who want to sell us something, which helps us stay vigilant against those who want to manipulate us.

**existential import** – The property of a proposition that implies that something exists. For example, Aristotle thought that the proposition “all animals are mammals” implied that “at least one mammal exists.” However, many logicians now argue that propositions of this type do not have existential import. See the “existential fallacy” for more information.

**expressibility** – The ability of a logical system to express the meaning of our statements. For example, consider the argument, “all humans are mammals; all mammals are animals; therefore, all humans are animals. According to propositional logic, this argument has the form “*A*; *B*; therefore, *C*” and it would determine this argument to be logically invalid as a result. However, predicate logic is better able to capture the meaning of these statements and it can prove that the argument is logically valid after all. Therefore, predicate logic is expressively superior to propositional logic given this one example. See “valid argument” for more information.

**expressive completeness** – A logical system is expressively complete if it can state everything it is meant to express. For example, a system of propositional logic with connectives for “and” and “not” is expressively complete insofar as it can state everything any other connective could state. You can restate “*A* and/or *B*” as “it’s not the case that both not-*A* and not-*B*.” (“Hypatia is a mammal and/or a mortal” means the same thing as “it’s not the case that Hypatia is both a non-mammal and a non-mortal.”) See “expressibility” and “logical connective” for more information.

**formal semantics** – A domain concerned with the interpretations of formal propositions. For example, “*A* and *B*” could be interpreted as “all lizards are reptiles and all dogs are mammals.” (“*A*” and “*B*” each represent specific propositions.) See “interpretation,” “translation,” “models,” and “schemes of abbreviation” for more information.

**function** – A synonym for “operation.”

**good argument** – An argument that’s rationally persuasive. A popular example of a good argument is “Socrates is a man. All men are mortal. Therefore, Socrates is mortal.” Good arguments give us a good reason to believe a conclusion is true. If an argument is sufficiently good, then we should believe the conclusion is true. Ideally good arguments rationally require us to believe the conclusion is true, but some arguments might only be good enough to assure us that a belief is compatible with rationality. The criteria used to determine when an argument is “good” is studied by logicians and philosophers.

**grouping** – In logic, grouping is used to make it clear how logical connectives relate to various propositions, and parentheses are often used. For example, “*A* or (*B* and *C*)” groups “*B* and *C*” together. In this case “*A*” can stand for “George Washington was the first president of the United States,” “*B*” can stand for “George Washington is a mammal,” and “*C*” can stand for “George Washington is a lizard.” In this case the statement can be interpreted as “George Washington is a lizard, or he is both a mammal and a lizard.” This can be contrasted with the statement “(*A* or *B*) and *C*,” which would be interpreted as “George Washington is either the first president of the United States or a mammal, and he’s a lizard.”

**halt** – (1) When a mechanical procedure ends. For example, we can use truth tables to know if arguments are valid. The procedure halts as soon as we determine whether or not the argument is valid. See “valid argument” and “truth table” for more information. (2) In ordinary language, ‘halt’ means “stop.”

**index of points** – A set of points. Some philosophers believe that the truth conditions of *necessity* and *possibility* are based on an index of points. Aristotle thought that something was necessary if and only if it is true at all times, and possible if and only if it is true at some time. It’s necessary that “1+1=2” because it’s true at all times, and it’s possible for a person to jump over a small rock because it’s true at some time. In this case the index of points refers to points in time. See “truth conditions” for more information.

**inductive validity** – A synonym for “strong argument.”

**interpretation** – (1) To attribute meaning to statements of a formal logical system. Formal logical statements are devoid of content, but we can add content to them in order to transform them into statements of natural language. For example, “*A* or *B*” is a statement of a formal logical system, and it can be interpreted as stating, “either evolution is true or creationism is true.” In this case “*A*” stands for “evolution is true” an “*B*” stands for “creationism is true.” See “formal semantics,” “models,” and “schemes of abbreviation” for more information. (2) In ordinary language “interpretation” refers to the act of taking statements of one language and translating them into statements of another language.

**law of nature** – (1) A constant predictable element of nature. For example, the law of gravity states that dropped objects will fall when dropped near the surface of the Earth. (2) A synonym for “natural law.”

**lemma** – A proven statement used to prove other statements.

**letter** – (1) A symbol used from an alphabet in symbolic logic. See “predicate letter” and “propositional letter” for more information. (2) A symbol used in an alphabet, such as “A, B, [and] C.” (3) A message written on a piece of paper for the purposes of communication over a distance.

**Liebnitz’s law** – The view that there can’t be two or more different entities that have the exact same properties. For example, two seemingly identical marbles are both made of different atoms and exist at different places. Two entities that have all the same properties would both have to exist at the same place at the same time. Imagine that we find out that Clark Kent was at the same place and the same time as Superman. That seems like a good reason to think that Clark Kent is Superman because Clark Kent and Superman can’t have all the same properties and be two different people.

**logical constant** – Symbols used in formal logic that always mean the same thing. Logical connectives and quantifiers are examples of logical constants. For example, “∧” is a logical connective that means “and.” See “logical connective” and “quantifier” for more information. “Logical constants” can be contrasted with “predicate constants.”

**logical system** – A system with axioms and rules of inference that can be applied to statements in order to determine if propositions are consistent, tautological, or contradictory. Additionally, logical systems are used to determine if arguments are logically valid. See “formal logic,” “axioms,” and “rules of inference” for more information.

**main connective** – A logical connective that’s inside the least amount of parentheses when put into a formal language. For example, consider the statement “all dogs are mammals or reptiles, and all dogs are animals.” This statement has the propositional form “(A or B) and C.” In this case “and” is the main connective. See “formal logic,” “logical connective,” and “grouping” for more information.

**master table** – A truth table that defines all logical connectives used by a logical system by stating every combination of truth values, and the truth value of propositions that use the logical connectives. For example, the logical connective “a ∧ b” means “*a* and *b*,” so it’s true if and only if both *a* and *b* are true. (“Hypatia is a mammal and a person” is true because she is both a mammal and a person. See “logical connective” for more information.) An example of a master table for propositional logic is the following:

**maximally complete** – See “syntactic completeness.”

**metalogic** – The study of logical systems. Logic is concerned with using logical systems to determine validity, and metalogic is concerned with determining the properties of entire logical systems. For example, a logical system can be “expressively complete.”

**methodological naturalism** – See “epistemic naturalism.”

**modal antirealism** – The view that there are no modal facts—facts concerning necessity and possibility. For example, a modal antirealist would say that it’s not a fact that it’s possible for a person to jump over a small rock.

**modal realism** – The view that there are modal facts—facts concerning necessity and possibility. For example, it seems like a fact that it’s possible for a person to jump over a small rock; and it seems like a fact that it’s necessary that contradictions don’t exist. See “modality,” “concretism,” and “abstractism” for more information.

**moral objectivism** – (1) The view that there are moral facts that are mind-independent as opposed to forms of moral realism that depend on subjective states or conventions. This form of moral objectivism requires a rejection of “moral subjectivism” and “constructivism.” See “moral realism” for more information. (2) A synonym for “moral realism.”

**NAND** – See “Sheffer stroke.”

**natural law** – (1) A theory of ethics that states that moral standards are determined by facts of nature. Consider the following two examples: One, the fact that human beings need food to live could determine that it’s wrong to prevent people from eating food. Two, the fact that people have a natural desire to care for one another could be a good reason for them to do so. (2) A theory of ethics that states that there are objective moral standards. See “moral objectivism.” (3) A theory of law that states that laws should be created because of moral considerations. For example, murder should be illegal because it’s immoral.

**NOR** – See “Peirce stroke.”

**offensive** – A synonym for “suberogation.”

**omissible** – Not obligatory, but permissible. For example, jumping up and down is generally considered to be permissible and non-obligatory. “Omissible” is not a synonym of “permissible” because all obligatory actions are also taken to be permissible. “Omissible” can be contrasted with “obligatory” and “permissible.”

**operands** – The input involved with an operation or predicate. For example, “Gxy” is a statement of predicate logic with two operands—two things being predicated. “G” can stand for “jumps over.” In that case “Gxy” means “x jumps over y” and “x” and “y” are each an operands. See “predicate logic” and “operation” for more information.

**operation** – Something with variables, input, and output. For example, addition is a function with two different numbers as input, and another number that’s the output. You can input 1 and 3 and the output is 4. (1+3=4.) Statements of predicate logic are also said to involve an operation insofar as predicates are taken to be operations. For example, “Fj” is a statement of predicate logic that could also be taken to be an operation. In this case “F” could stand for “is intelligent” and “j” can stand for “Jennifer.” In that case the input is “j” and the output is “Jennifer is intelligent.” See “predicate logic” and “operands” for more information.

**Peirce stroke** – A symbol used in formal logic to mean “neither this-nor-that” or “not-*a* and not-*b*.” (“*a*” and “*b*” are any two propositions.) The symbol used is “↓.” For example, “all dogs are lizards ↓ all dogs are fish” means that “it’s not the case that all dogs are lizards, and it’s not the case that all dogs are fish.” See “formal logic” and “logical connective” for more information.

**philosophical logic** – Logical domains with a strong connection to philosophical issues, such as modal logic, epistemic logic, temporal logic, and deontic logic. “Philosophical logic” can be contrasted with “philosophy of logic.”

**philosophy of logic **– A philosophical domain concerned with issues of logic. For example, questions involving the role of logic, the nature of logic, and the nature of critical thinking. “Philosophy of logic” can be contrasted with “philosophical logic.”

**predicate constants** – Constants in predicate logic are specific things that are predicated. The lower case letters “a, b, [and] c” are commonly used. For example, consider the statement, “George Washington is an animal.” In this case we can write this statement in predicate logic as “Ag” where “A” means “is an animal” and “g” stands for “George Washington.” In this case “g” is a constant because it refers to something specific that’s being predicated. Sometimes variables are used instead of constants. For example, “Ax” means “x is an animal” and “x” can be anything. See “predicate logic,” “predicate variables,” and “predicate letters” for more information. “Predicate constants” can be contrasted with “logical constants.”

**predicate letters** – Capital letters used in predicate logic are used as symbols for predicates, and the letters generally used are F, G,and H. For example, “F” can stand for “is tall.” In that case “Fx” is a statement that means “x is tall.” See “predicate logic,” “relation letters,” “predicate constants,” and “predicate variables” for more information.

**predicate variables** – Variables in predicate logic are things that are predicated without anything in particular being mentioned. The lower-case letters “x, y, [and] z” are usually used. For example, consider the statement “it is an animal.” In this case “it” is something, but nothing in particular. It could be Lassie the dog, Socrates, or something else. We could write “it is an animal” in predicate logic with a variable as “Fx.” In this case “F” means “is an animal” and “x” is the variable. See “predicate logic,” “predicate letters” and “predicate constants” for more information. “Predicate variables” can be contrasted with “propositional variables.”

**propositional letter** – Symbols used to stand for specific propositions in propositional logic. Upper-case letters are often used. For example, “*A*” can stand for “George Washington was the first President of the United States.” “Propositional letters” can be contrasted with “propositional variables.” See “propositional logic” for more information.

**propositional variable** – Symbols that stand for any possible proposition in propositional logic. Lower-case letters are often used. For example, “*a*” can stand for any possible proposition. It can stand for “*A* or *B;*” or “*A* and *B*, or *C;*” etc. “Propositional variables” can be contrasted with “predicate variables.” See “propositional logic” for more information.

**reasoning** – The thought process that leads to an inference. For example, a person who knows that *all dogs are mammals* and that *Lassie is a dog* can come to the realization that *Lassie is a mammal*. Reasoning that’s made explicit along with the conclusion are “arguments.” One potential difference between reasoning and arguments is that reasoning does not necessarily include the inference, but arguments must include a conclusion. Everything we say about reasoning or arguments tends to correspond to both. For example, fallacious arguments corresponds to fallacious reasoning of the same type, logically valid arguments has a corresponding logically valid reasoning, etc. Moreover, inductive and deductive types of arguments correspond to inductive and deductive types of reasoning.

**reducibility** – To be able to express everything from one logical system in another. For example, a propositional logical system with the logical connectives for “and” and “not” can state everything said by other logical connectives. Therefore, a system of propositional logic that has logical connectives for “not,” “and,” “and/or,” “implies,” and “if and only if” can be reduced to a system that only has connectives for “and” and “not.” See “expressibility” and “logical connectives” for more information.

**relation letters** – Predicate letters used in predicate logic that involve two or more things that are predicated. Capital letters are used to represent predicates, and “F, G, [and] H” are most commonly used. For example, “F” can stand for “attacks.” In that case “Fxy” is a statement that means “x attacks y.” See “predicate logic,” “predicate letters,” “predicate constants,” and “predicate variables” for more information.

**rhetoric** – (1) Persuasion using ordinary language. In this sense both rational argumentation and fallacious argumentation could be considered to be forms of rhetoric. Rhetoric is the specialization of public speaking, persuasion used by lawyers, and oratory used by politicians. (2) Argumentation used for the purpose of persuasion. This type of rhetoric can involve technical terminology used by specialists. This type of rhetoric is compatible with both public speaking and essays written by philosophers. (3) Persuasion that uses nonrational forms of persuasion through language. Fallacious arguments, propaganda, and various forms of manipulation could be considered to be rhetoric in this sense. This type of rhetoric is thought to be a source of power for sophists, pseudoscience advocates, snake oil salesmen, and cult leaders.

**rhetorical arguments** – Arguments used for persuasion. Rhetorical arguments are thought to be very important in politics and in the court room. See “rhetoric” for more information.

**satisfiability** – The ability to interpret a set of statements of formal logic in a way that would make them true. Statements that can all be simultaneously interpreted as true in this way are satisfiable. Consider the statement “a → b.” In this case “a” and “b” stand for any propositions and “→” stands for “implies.” We can interpret “a” as being “all bats are mammals” and “b” as being “all bats are animals.” In that case we can interpret the whole statement as saying “if all bats are mammals, then all bats are animals,” which is a true statement. Therefore, “a → b” is satisfiable. See “formal logic” and “interpretation” for more information.

**semantic completeness** – A logical system is semantically complete if and only if it can prove everything it is supposed to be able to prove. For example, propositional logic is semantically complete insofar as it can be used to determine whether any possible argument is valid.

**semantics** – The meaning of words or propositions. “Semantics” can be contrasted with “syntax.”

**sentenial** – Something relating to sentences. For example, propositional logic is “sentenial.”

**sentential logic** – A synonym for “propositional logic.”

**Sheffer stroke** – A symbol used in propositional logic to mean “not both” or “it’s not the case that *a* and *b* are both false.” (“*a*” and “*b*” are any two propositions.) The symbol used is generally “|” or “↑.” For example, “Dogs are mammals ↑ dogs are lizards” means that “it is not the case that dogs are both mammals and lizards.”

**sound logical system** – A logical system is sound if every statement it can prove using the axioms and rules of inference is a tautology (a logical truth). See “tautology” for more information.

**statement letter** – See “propositional letter.”

**statement variable** – See “propositional variable.”

**suberogatory** – Actions or beliefs that are inferior to alternatives (or somewhat harmful), but are permissible. Suberogatory beliefs are compatible with rational requirements or normative epistemic constraints; and suberogatory actions are inferior to alternatives (or somewhat bad), but are compatible with moral requirements. For example, being rude is not generally serious enough to be “morally wrong,” but it is suberogatory. “Suberogatory” can be contrasted with “supererogatory.”

**subsentential** – Something relating to parts of sentences, such as predicate logic.

**subsentential logic** – A synonym for “predicate logic.”

**syllogism** – A deductive argument. For example, “Either George Washington was a person or a dog. George Washington was not a dog. Therefore, George Washington was a person.”

**syntactic completeness** – A logical system is syntactically complete if it has every axiom it needs. Adding an unprovable axiom to a syntactically complete logical system will produce at least one contradiction.

**syntax** – The arrangement of words or symbols. Syntax can involve rules and symbol manipulation, and formal logic can be considered to mainly involve syntax for that reason. “Syntax” can be contrasted with “semantics.”

**temporal interpretation of modality** – The view that “necessity” and “possibility” are based on time. For something to be necessary is for it to be true of all times, and for something to be possible is for it to be true at some time. It’s necessary that dogs are mammals because dogs are mammals at all times, and it’s possible for it to rain because there is at least one time that it rains. See “modality” and “truth conditions” for more information. The “temporal interpretation of modality” can be contrasted with the “worlds interpretation of modality.”

**theorem** – A statement that we can know is true because of the axioms and rules of inference of a logical system. For example, consider a logical system with “*a* or not-*a*” as an axiom and the rule of inference that “*a* implies *a* or *b*.” The following is a proof of that system—“*A* or not-*A*. Therefore, *A* or not-*A*, or *B*.” In this case “*A* or not-*A*, or *B*” is a theorem. See “derivation,” “axioms,” “rules of inference,” and “logical system” for more information.

**trans-world identity** – For something to exist in multiple worlds. Some philosophers talk about there being multiple possible worlds. For example, they might say that it was possible for *George Washington to become the King of the United States* because *there’s a possible world where he became the king*. In this case we could say that George Washington has trans-world identity because he exists in multiple possible worlds. “Trans-world identity” can be contrasted to “world-bound individuals.” See “modality” and “possible world” for more information.

**translation** – (1) The restatement of a statement in natural language to a statement of formal logic. For example, “either George Washington was a dog or a mammal” can be translated into propositional logic as “P ∨ Q,” where “P” stands for “George Washington was a dog” and “Q” stands for “George Washington was a mammal” and “∨” is a logical connective meaning “and/or.” See “logical form” for more information. (2) In ordinary language, translation refers to a restatement of a sentence (or set of sentences). For example, the sentence “Il pleut” can be translated from French to English as “It’s raining.”

**truth conditions** – The conditions that make a statement true. For example, the truth condition of “the cat is on the mat” is a cat on a mat. The statement is true if and only if a cat is on a mat. Sometimes truth conditions are controversial, such as when we say it’s “necessary that people are rational animals.” It could be true if and only if people are rational animals in all times, or in all possible worlds, or perhaps given some other condition.

**Turing machine** – A symbol manipulation machine that follows rules in order to make movements. Such a machine can do logical and mathematical operations. Turing machines were originally hypothetical devices, but computers could be considered to be Turing machines.

**Turing test** – A test used to examine the ability of a machine to speak natural language within a conversation. Machines that speak natural language within conversations in exactly the same way as real human beings pass the Turing test. Any machine that passes the Turing test could be said to adequately simulate human behavior in regards to its ability to simulate a conversation in natural language. There could be tests similar to the Turing test that tests a machine’s ability to simulate other types of human behavior.

**valid formula** – A valid statement. A statement that is true under all interpretations. For example, “*A* or not-*A*” is true no matter what proposition “*A*” stands for. If “*A*” stands for “nothing exists,” then the statement is “either nothing exists or it’s not the case that nothing exists.” In propositional logic, “valid formula” is a synonym for “tautology.”

**valid logical system** – A logical system that has valid rules of inference. If a logical system is valid, then it’s impossible for true premises to be used with the rules of inference to prove a false conclusion. See “rules of inference” for more information.

**variable** – (1) See “propositional variable” or “predicate variable.” (2) A symbol used to represent something else, or a symbol used to represent a range of possible things. For example, “x + 3 = y” has two variables that can represent a range of possible things (“x” and “y.”)

**world-bound individuals** – For something to only exist in one world. Some philosophers talk about there being multiple possible worlds, but they think each person is world-bound insofar as they can only exist in one world. For example, they might say that it was possible for Thomas Jefferson to become the first President of the United States because there’s a possible world where the person in that world who most resembles Thomas Jefferson became the first President of the United States. That possible world does not contain the actual Thomas Jefferson in it. “Trans-world identity” can be contrasted with “world-bound individuals.” See “modality” and “possible world” for more information.

**worlds interpretation of modality** – A view of “necessity” and “possibility” based on worlds. For something to be necessary is for it to be true of all worlds, and for something to be possible is for it to be true at some world. It’s necessary that dogs are mammals because dogs are mammals at all words, and it’s possible for it to rain because there’s at least one world that it rains. The “worlds interpretation of modality” can be contrasted with the “temporal interpretation of modality.” See “possible worlds” and “modality” for more information.

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